There was nothing out-of-sorts about the Owls' second-half comeback.
And they nearly condemned Bristol City to a first home league defeat of 2009 after Varney's fine strike with 15 minutes left cancelled out Nicky Maynard's 59th-minute opener.
Rocking Robins are still fifth but boss Gary Johnson admits his side did not look like play-off challengers here.
Sick Owls were without five players and included two in their squad who were still ill.
Johnson said: "That was us nicking a point because we should have lost. My players have a week to turn it around and that will tell us where we are.
"We didn't look like where we are in the league with that performance.
"I want us to start competing for the top two but I hardly recognised my team out there and I'm grateful for a point.
"We looked all over the shop and we haven't looked like that for a long time.
"It was a bit of a surprise. We are in a state and we have got to sort it out. But it's good to be in a state in fifth place.
"They will be moaning they had 'flu but sometimes things like that can pull a team together."
Wednesday chief Brian Laws hopes earning this draw with a depleted squad will be a turning point after three defeats in their previous four games.
The visitors even notified the Football League about the illness yesterday.
Laws said: "Under the circumstances, I would have been happy with a point before the game. But after it, I think we deserved all three because we had the better chances.
"We can use this as a turning point because it was a test of character and we did really well. It showed what we are about and we worked really hard for it.
"We asked the Football League for advice and phoned the hotel to make sure they had a doctor on site. But there was never any danger of the game being called off.
"Perhaps people thought we might be looking for a bit of sympathy. Did Bristol City approach the game thinking it was going to be easy after they heard our problems?
"We went from Plan A to Plan F because we had so many problems with players out.
"We had five first-team players out and two in the squad were carrying it or recovering from it. I don't know whether it's swine 'flu. It's just something that has gone around the club and Tommy Miller was physically sick at half-time."
On-loan Derby striker Varney produced a precision finish but he did not look the same player earlier when he tamely hit his shot straight at City keeper Dean Gerken from 12 yards on 37 minutes.
Two minutes later, Jamaica international Jermaine Johnson - who signed a new two-year deal last week - created havoc amid the rocky City defence.
He rolled the ball invitingly into the penalty area into the path of Marcus Tudgay.
But just as the Owls striker was about to pull the trigger, an immaculately timed tackle from Louis Carey foiled the chance.
City had looked the likelier to score early on when in-form Maynard sharply turned and drove a low shot from the edge of the area that Lee Grant did well to hold after half-an-hour.
Johnson made two changes at half-time to make his side more creative and threatening.
He replaced his son Lee with Paul Hartley and sent on Costa Rican striker Alvaro Saborio for skipper Carey.
The result was an improvement in attack, initially at least.
Maynard claimed a scrappy 10th goal of the season when he doggedly broke through two tackles en route to poking past Lee Grant after Wednesday had allowed the ball to fizz around their penalty area without clearing.
Ten minutes later, Gerken made a breathtaking reflex save when he dropped to his right to push away Leon Clarke's shot from close in.
Laws thought Wednesday were denied a penalty when Richard Hinds was floored by Jamie McCombe on 70 minutes.
The Owls boss said: "I thought it was a blatant penalty - but the ref said he slipped."
But the visitors deservedly drew level five minutes later when Varney scampered on to Tudgay's pass before belting low into the corner from 20 yards.
Both sides went for the winner with Gerken making stunning saves to keep out Varney and Clarke's audacious chip in injury-time.
This article has 0 comments