It was back-to-back promotions for the Grecians as they finished off the season with a nervy victory over ten-man Rotherham.
The home side played the last 16 minutes without Dale Tonge after he was sent off for bringing down Craig McAllister in the area.
But Stuart Fleetwood's resulting penalty was easily saved by keeper Andy Warrington.
Exeter were struggling to find a way through and Rotherham had looked more likely to score.
Then Logan arrived on cue at the far post to guide a looping header over Warrington in the 70th minute after Rob Edwards picked him out.
Delighted Exeter boss Paul Tisdale admitted he was receiving messages from a spy watching Bury, who had a chance of pipping Exeter to automatic promotion.
Tisdale said: "We had somebody there with a mobile phone and made sure he charged it before he went.
"We knew the trickiest situation for us would be 0-0 with us and 0-0 with them with minutes remaining.
"It nearly got to that point. Then we got our goal and started listening very carefully to what was going on at the other end.
"I still didn't know their scoreline because we knew our win meant we'd clinched it for ourselves.
"It's a great achievement for everyone at the club and we'll enjoy it before we discuss next year.
"Since the day we went down into the Conference it has been a long slog back. This is down to a lot of hard work and doing things in a slow but steady fashion."
Rotherham boss Mark Robins said: "It was a disappointing way to end a season which has been magnificent considering we started with a 17-point deduction. We didn't want to join somebody else's promotion party but congratulations to Exeter.
"They were outstanding. They needed points for promotion and it certainly showed in their play."
Exeter were fortunate to reach half time on level terms after Rotherham created a handful of opportunities.
Striker Reuben Reid hoisted a difficult effort over and when Mark Hudson's long ball sent Drewe Broughton charging through, the big front man looked sure to score after rounding keeper Paul Jones.
Exeter's Troy Archibald-Henville came to the rescue, racing back to hook the a ball off the line.
Seconds before the break Exeter were a fraction away from conceding but Paul Jones fingertipped Jamie Green's cross onto the bar.
The travelling fans had to wait until 20 minutes from time to celebrate as Logan rose at the far post to head in.
WYCOMBE were promoted despite this defeat in a dramatic finale and suffering boss Peter Taylor admitted: "We crawled over the line - and I'm knackered!"
The Chairboys squeezed into the automatic promotion places by pipping Bury to third place on goal difference of ONE after the Shakers beat Accrington 1-0 to finish level on points with Taylor's team.
But Wycombe had to wait for five minutes before they finally got confirmation they were promoted.
Taylor, who went into the dressing-room rather than wait on the pitch for the final score to come through from Gigg Lane, said: "It was the longest five minutes in the world.
"But, thankfully, the news came through that we were up.
"I've never experienced such a tight finish. But promotions aren't won in one game, they are won over a long, hard season. We finished third and we deserved to finish third." Taylor told the crowd: "It's been a fantastic season. We wanted to win promotion in front of a full house but now I'm knackered!"
John Thompson's 35- yarder put County ahead on 31 minutes but skipper David McCracken levelled just after the break.
But Thompson's second long-ranger won it for County to leave Wycombe waiting on the result from Gigg Lane.
PAUL SIMPSON is ready to heap more misery on play-off opponents Bury after Shrews' dramatic win-or-bust win.
Wing wizard Chris Humphrey scored one and made the other as Town leapfrogged hosts Dagenham to pinch the crucial seventh spot.
Shrews' win teed up Thursday's play-off semi-final first leg at home to Bury, who suffered the agony of missing out on automatic promotion to Wycombe by just one goal's difference.
Town boss Simpson said: "I'm sure Bury will be disappointed they didn't go up - they're a good side.
"They're the fourth-best team in the league - but if we play as we're capable of, we'll give anyone a game.
"We need to go there and do the job properly. What happened in the 45 games before today counted for nothing.
"Now we've got a two-legged game. We'll take a lot of confidence from this performance. Now it's about who can deal with these next two games."
Humphrey crossed for Grant Holt to head his 28th goal of the season on 18 minutes and then Humphrey lobbed in the second on 33 minutes. Daggers striker Paul Benson hit the post and pulled one back with his 21st goal this term after 53 minutes.
But the visitors held on to spark a full-time pitch invasion despite the efforts of police and stewards.
Daggers manager John Still toasted his side's best-ever league finish despite the heartache.
He said: "I'm disappointed to get beat but so proud of the players to come this far. It's phenomenal to finish where we did and that's credit to our players.
"It's our Player of the Year do tonight and I'll have as much as possible to drink and look back on a great season."
Daggers' League record crowd of 4,791 saw home striker Benson bundled off the ball as he burst goalwards after 10 minutes.
The Shrews took over with Humphrey skipping free to cross for Nick Chadwick, who forced veteran Daggers keeper Tony Roberts into a brilliant point-blank double save.
Town striker Holt made no mistake when Humphrey delivered his next cross - heading home from eight yards for the opener.
Kelvin Langmead kept the visitors in front, blocking Matt Ritchie's shot, before Humphrey slammed a volley at Roberts, drawing another great parry.
Humphrey stayed ice-cool to put Shrewsbury 2-0 up, lobbing the onrushing Roberts from 16 yards.
Sam Saunders headed wide from a corner while, after the break, Benson hit the post from in front of goal, Luke Daniels saving Ben Strevens' follow-up.
Benson pulled a goal back after 53 minutes, rising highest to meet Ritchie's cross.
Holt scuffed a great chance wide from Chadwick's cross with 20 minutes left and then Chadwick was denied by another Roberts save.
SHAKERS fans were left shaking with anger after finishing a goal short of automatic promotion.
Bury players and officials complained about the lost three minutes of added time which referee Andy D'Urso failed to play after a penalty drama and sending off in extra time.
Home fans ran on to the Gigg Lane pitch after sub Phil Jevons swept in the spot-kick but they were unaware that other results meant they were destined for the play-offs.
Referee D'Urso had added five minutes and, following long consultation with a linesman, he awarded a penalty to Bury after Stanley's Andy Proctor handled Ben Futcher's header on the line. Proctor was red carded and with around three minutes left, the referee blew the final whistle and ran off.
It was Bury's 12th unbeaten game on the trot and boss Alan Knill said: "There should have been more time at the end. We might have got another goal."
D'Urso had earlier awarded Stanley a penalty, ruling keeper Wayne Brown had brought down sub Chris Turner. But Peter Cavanagh's spot kick hit the bar and Bury survived.
DAVE FLITCROFT was accused of roughing up Gillingham players ahead of Thursday's play-offs rematch at Spotland.
The Dale assistant boss - now 35 and carrying weight - made his first appearance of the season as a second-half sub.
He was booked within four minutes for clattering Gills winger Albert Jarrett.
Gills boss Mark Stimson said: "Albert's ankle is swollen. The guy that came on was trying his hardest to put someone out of the semis. I could have done what he did but if you're not playing regularly, then don't get involved."
Dale boss Keith Hill hit back, saying: "David Flitcroft didn't go on to harm anybody. We put him on as a mark of respect for what he's done for this club."
Curtis Weston's close-range strike settled matters in the 20th minute.
BRENTFORD imposed their own version of Newton's Law of Gravity as Luton ended their Football League career on a low.
Adam Newton hit a stunning second goal as Bees went up to League One - and Town down to the Blue Square Premier.
It was party time for the home fans with fireworks on the pitch as Andy Scott's champs lifted their trophy. But Luton crashed out of the League with a whimper after 89 years.
Hatters fans chanted 'We'll be back' but boss Mick Harford and his players made a shame- faced exit from Griffin Park.
Scott said: "I've had a fantastic first full season in charge - now I want to get Brentford into the Championship.
"We are off to Las Vegas next week, and the players will enjoy it - lifting the trophy today felt extra-special."
Luton had threatened to dampen the home side's celebrations as keeper Dean Brill denied Billy Clarke and kept the score blank for 72 minutes.
But Bees finally broke through when sub Karleigh Osborne nodded in David Hunt's free kick.
And Hunt set up Newton to curl home an 18-yard cracker for his first goal of the season.
PORT VALE chairman Bill Bratt revealed that former Carlisle boss John Ward is "in the frame" to replace Dean Glover as manager.
Glover's last match in charge after a stormy seven months came too late to save his position, even though his efforts saved the Valiants' league status.
Bratt said: "Dean was a hero of mine as a player but we expected more from him. It's a difficult job and everybody's got the utmost respect for him but we have to think of what's best for the club.''
Glover's son Danny helped dad sign off in style. Louis Dodds gave the Valiants a 10th-minute lead before Glover junior drove home a rebound after his penalty-kick had been saved in first-half injury time. Barnet's Abu Ogogo was sent off after handling his first effort.
Danny Hart reduced the arrears in injury time.
Barnet boss Ian Hendon said: "I have offered Paul Furlong a year's deal for next season. He's 40 but capable of playing on."
CHESTER'S relegation to non-league football was confirmed yesterday after two goals from Darlington's Pawel Abbott.
City, rumoured to be close to financial administration, went behind after 71 minutes when Abbott rifled home from close range after keeper James Spencer had been forced to save a back-pass from Glenn Rule on his six-yard line.
Two minutes from the end, Ian Miller rocketed a header into his own net to equalise for City following Anthony Barry's cross from the right.
Two minutes into added time, Abbott hit the winner when a mistake by Kevin Roberts gifted the striker his second.
City boss Mark Wright said: "Relegation is hard to take but already I have spoken to the chairman and we have a number of players that we have pencilled in."
Darlington assistant boss Martin Gray said: "Pawel is top quality. He took his goals extremely well."
VETERAN striker Geoff Horsfield wasted a hat-trick of chances in what may be his final league game.
The 35-year-old, given a new chance by Lincoln after beating cancer last year, just could not find the net. And his side paid the price as the Shots ended up outplaying the home team.
Aldershot's Scott Donnelly hit the post early on before Horsfield was twice put clear but failed to beat the keeper.
John Grant put Aldershot in front in the 26th minute with a glancing header but Horsfield should have equalised in stoppage time when he was left unmarked but could not get in a shot.
Horsfield was replaced at the break and Aldershot went on to grab a late second goal when Scott Davies struck from 25 yards.
Lincoln manager Peter Jackson said: "We created enough chances to win two games but we didn't take them. It's been a really frustrating season."
LEE RICHARDSON was again targeted by angry fans to leave his job as Chesterfield boss hanging in the balance.
Supporters chanted "Rico out" as they missed out on the play- offs for a second successive year.
Richardson's contract is up next month and he said: "We'll see if the chairman and board are happy or whether they bow to the pressure of a percentage of supporters.
"It's the second time on the trot we've missed out narrowly. I've been in charge for those two seasons and in some people's eyes it's simple where the blame lies."
Bradford boss Stuart McCall hopes to keep on-loan Glasgow Rangers midfielder Dean Furman next season.
McCall said: "I will do anything I possibly can to keep him. He's an outstanding person."
Furman got the opener on 54 minutes from a Nicky Law cross and Michael Boulding smashed his 13th of the campaign to settle it two minutes from time.
BOURNEMOUTH striker Brett Pitman ended the season in style with a double in his side's best away win of the season.
Pitman took his tally to 18 with a goal in each half to boost the Cherries, who had laboured under a 17-point deduction.
It did not spare Pitman a telling off for showing disgust at being substituted late on.
Boss Eddie Howe said: "I told Brett that this is a team game and I wanted to hand George Webb his debut."
Howe's side were handed a dream start when defender Josh Ward beat static Morecambe keeper Barry Roche to Danny Hollands' inswinging corner.
Liam Feeney's superb strike made it 2-0 in the 35th minute and Pitman opened his account just before the interval.
The Cherries hitman grabbed his second at the far post in the 69th minute.
Morecambe skipper Jim Bentley groaned: "We let the fans down."
GRIMSBY boss Mike Newell has promised fans there will be no repeat of this season's struggle with relegation.
The Mariners ensured their survival after a bore draw at Blundell Park but Newell insists changes will be made.
Newell, who took over from Alan Buckley in October, said: "I can't see us having this much trouble again.
"It's as important as any of the highs I've achieved in football to secure safety but I know there's a long job here. The first part was keeping the club up.''
Gareth Evans squandered Macclesfield's best chance in the first half when he fired straight at keeper Wayne Henderson.
But Grimsby's Jean-Louis Akpa Akpro and Adam Proudlock both forced smart saves from Jonny Brain after the break.
Silkmen boss Keith Alexander said: "I'm delighted with a point - and with the way we've played in the last three or four games."
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