Midfielder Moxey fired a hopeful 30-yard ball into the box with time running out. Lincoln keeper Rob Burch made a hash of the catch and was left red-faced as the ball bounced back off a post and in off his body.
The 88th-minute goal leaves Grecians boss Paul Tisdale eyeing promotion for a second season running.
He admitted: "We were a bit fortuitous with the goal but we'll take everything we can at the moment. It's a massive three points for us. Our fate is in our own hands now.
"In the last 20 minutes we gave it a real go. We put a lot more balls into dangerous positions and although it wasn't pretty at times it gave us a chance.
"It was all about the result. The fact we got three points and scored so late in the game will be a blow to the teams behind us."
Lincoln went closest to breaking the deadlock in the first half with efforts by Andy Hutchinson and Janos Kovacs.
But Exeter were more dangerous after the break. Craig McAllister saw his 64th-minute effort cleared off the line by Scott Kerr and McAllister then set up a chance for Stuart Fleetwood.
But Paul Jones kept Exeter on terms with an excellent save to deny Nathan Adams a goal on his debut.
Lincoln boss Peter Jackson said: "I thought we defended terrifically all game. We are bitterly disappointed."
ANDY SCOTT is one win away from promotion after this romp.
Brentford were on cruise control after Sam Williams headed them in front after eight minutes.
Ryan Dickson got No 2 just after the break and Billy Clarke banged home his fourth goal in four games with a penalty after Kieran Charnock felled Williams.
Wins for Exeter, Wycombe and Bury kept Brentford waiting to uncork their bubbly.
But boss Scott said: "I told the lads I didn't care what anyone else was doing. We had to do our job."
Stanley boss John Coleman risked playing Paul Cavanagh and Robbie Williams - who face FA charges over betting irregularities. He said: "I wanted to be loyal to the league and play my strongest side."
CHESTER need a miracle to stay up after crashing to fellow-strugglers Bournemouth.
Mark Wright's men must now win at Aldershot on Saturday and at home to Darlington in their final game - and hope next weekend's clash between Cherries and Grimsby does not end in a draw!
Wright admitted: "Bournemouth deserved to win - we were always up against it after their early goal.
"They were bigger in most departments than we were and our team which included a number of youngsters couldn't cope. Now we have to move on to Aldershot next week and try to get a victory - and hope other results go our way."
Bournemouth, who look set to stay up despite starting the season with a 17-point deduction, were rarely troubled after Brett Pitman's third-minute free-kick for the opener.
Ryan Lowe scooped City's best chance for an equaliser over from close-range.
And Bournemouth wrapped up the points 11 minutes from time when Anton Robinson scrambled the ball home.
Cherries' assistant boss Jason Tindall said: "The game was in the balance at 1-0 but we relaxed a bit after the second goal went in."
ALAN KNILL is determined to prove the doubters wrong by clinching promotion.
Andy Bishop's early opener and Glynn Hurst's second-half double kept the Shakers in fourth spot.
Boss Knill said: "No one would have put us in the play-offs at the start of season, except us. But we're still going for the big prize."
Nat Brown left top scorer Bishop unmarked to head his 18th goal of the season.
Hurst side-footed in from Elliott Bennett's pass before turning in his eighth of the season and his fourth in three games.
Macclesfield manager Keith Alexander said: "We've got no leaders and I'm pleased that most of the squad are out of contract this summer."
JOHN AKINDE scored his sixth goal in eight games to edge Wycombe nearer automatic promotion.
Striker Akinde, on loan from Bristol City, rammed in a seventh- minute shot after Aldershot defender Dean Howell headed Jon-Paul Pittman's cross against his own post.
Wycombe grabbed a second on 52 minutes. Pittman's shot hit keeper Nikki Bull - only to go in off Ricky Newman's chest.
Wycombe made it 3-0 on 67 minutes, Matt Phillips slamming in Pittman's low cross.
Shots keeper Bull made a fine double save to deny efforts from Akinde and midfielder Lee Sawyer.
Aldershot's best chances were an Andy Sandell header hacked off the line by Craig Woodman, and John Grant's shot which Jamie Young tipped away for a corner.
JASON KENNEDY added another memorable moment to his repertoire against Rochdale.
The Darlington midfielder cracked home a stunning opener after just five minutes.
He also hit a cracker in last season's play-off clash against the Spotland side - but missed in the penalty shootout.
Kennedy beamed: "This goal was among my best. I wanted to come back here and make up for last season."
Rory McArdle's own goal settled it on 65 minutes after Pawel Abbott's header hit the bar and went in off the Dale defender.
Disappointed Dale boss Keith Hill said: "Their first was a wonder goal and the second killed us. We have no chance of automatic promotion now and must prepare for the play-offs."
BARRY CONLON scored two to give Grimsby the sniff of survival.
The on-loan Bradford forward grabbed a goal at the beginning of each half, either side of Nathan Jarman's effort, to move Mike Newell's men four points clear of the drop zone with two to play.
Conlon crashed his opener from close range after just four minutes.
Jarman's superb 21st-minute volley doubled the lead as he let fly from the edge of the box.
Vale's travelling fans had little to shout about until five minutes before the break when on-loan Manchester City midfielder Paul Marshall sent a dipping left-footer on to the top of the bar.
But Conlon bagged his fifth goal in six games just after the break when he pounced after keeper Chris Martin had fumbled Jarman's cross.
GILLINGHAM survived a mauling in the second half to keep their automatic promotion hopes alive thanks to Mark McCammon's fifth goal of the season.
McCammon struck in the 22nd minute.
Chesterfield failed to clear a corner, John Nutter whipped the ball back in and McCammon's powerful header went in off the underside of the bar.
There was little to worry the visitors until Drew Talbot got in on the right on 63 minutes and forced Simon Royce to make the first of two crucial saves.
The Gills had a lucky escape five minutes later when Kevin Austin headed against a post.
And Royce rescued them again on 78 minutes when Jack Lester's shot was superbly blocked by the keeper.
KEVIN NICHOLLS' red card was the only blot on a battling performance by relegated Luton.
Hatters' captain had already been booked when he tangled with Barnet's Yannick Bolasie.
The home side led on the stroke of half-time when Dean Brill pushed Gary Brean's header against a post and Adam Birchall tapped in.
But Luton levelled just after the break when Bees keeper Lee Harrison was left stranded and Rossi Jarvis was first to the loose ball.
DAGENHAM blitzed Bradford to boost their play-off hopes - and leave Bantams' hopes in tatters.
Sam Saunders broke the deadlock with a 20-yard stunner on 57 minutes. Paul Benson slotted No 2 on the end of Ben Strevens' pass 10 minutes from time and Strevens pounced on keeper Rhys Evans' fumble to make it 3-0 five minutes later.
Bantams slumped to 11th while Daggers could climb into the top seven if they beat leaders Brentford on Tuesday night.
SHREWSBURY shook off their awayday blues to chalk up only their second road win all season.
But they needed an own goal by Rotherham defender Ian Sharps to nick it after Ryan Taylor had cancelled out Nick Chadwick's opener.
Chadwick drilled in a low shot a minute before half-time. But Rotherham levelled 20 minutes from time when Taylor clipped in a low shot.
Six minutes later Sharps attempted to clear Neil Ashton's low cross but sliced into his own net.
MARK DUFFY hit his first goal for Morecambe to keep Shrimps' play-off hopes alive.
The former Southport man latched on to a loose ball to break the deadlock on 71 minutes.
And keeper Barry Roche pulled off a string of fine saves - capped by a stunning stop to keep out a header by County's Richard Butcher.
Morecambe came close to netting a second when Magpies keeper Kevin Pilkington denied Garry Hunter and Michael Twiss late on.
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