Marquis' fourth minute goal for Lincoln in the first half was cancelled out by Saido Berahino's strike in the first half, but goals from Brooke Norton-Cuffy and Marquis again secured a vital win for The Imps.
Story of the match
The Imps got themselves off to the perfect start as Marquis was able to knock the ball in from a corner to give the hosts the lead after just four minutes.
Liam Palmer had to be alert to stop the striker doubling his tally for the day inside the first eight minutes, as he intercepted a pass which which would have played Marquis in on goal.
Lincoln had to scramble clear a corner after Bannan volleyed the ball goalwards following a weak clearance from a corner.
The English midfielder then saw another shot go behind for a corner, which came to nothing for The Owls.
Palmer then lined up a shot, but it went high and wide of the target.
Morgan Whittaker had a chance to double the lead for Michael Appleton's side, as the ball was cut back to him from the byline, but his shot rolled wide.
Whittaker's cut back to Marquis was just too long, with the striker unmarked in the box to receive the ball.
Callum Paterson had the chance to level the tie, but the ball was taken off his foot as he went to shoot, and the resulting corner came to nothing.
Bannan's shot from range was deflected just over the bar, which the Wednesday captain was furious to see given as a goal kick to the hosts.
Wednesday had a deserved equaliser in the 32nd minute, as Johnson went on a superb run, beating several players and then picking out Berahino who volleyed home the equaliser.
Regan Poole then had a shot from inside the box, but Peacock-Farrell was able to save it.
Paterson then had a chance at the other end, as his strike took a deflection which left Lincoln goalkeeper Josh Griffiths rooted to the spot, but it rolled just behind for a corner which Wednesday could do nothing with.
Lewis Fiorini attempted an ambitious volley from range, but his effort swerved its way over.
Peacock-Farrell was fortunate not to be punished in added time, when he spilled a shot which Whittaker could not capitalise on.
The game was level at the break with Wednesday having more chances but it was a game which had seen both sides have opportunities to double their tallies, making for an entertaining first 45 minutes.
Half time score: Lincoln City 1-1 Sheffield Wednesday
Peacock-Farrell was just about able to claim a corner which he dropped initially.
He was then on hand to palm away a free kick from Maguire from the edge of the box.
Brooke Norton-Cuffy then got his first goal for Lincoln to put the hosts back in front.
Marquis cut the ball back to him, and he calmly slotted the ball into the bottom left hand corner to restore The Imps' lead.
Darren Moore then brought on top scorer Lee Gregory, who returned from injury to try and recover the game for his side.
Fiorini had a shot from range for the hosts which went just wide.
Tom Hopper found himself in on goal and managed to beat Peacock-Farrell with his effort, but Sam Hutchinson was on the line to head the ball over the bar.
Marquis then had his second of the game in the 76th minute, as he drilled his shot into the bottom left hand corner to give Lincoln breathing space in the tie.
Wednesday had the chance to claw one back in the final ten minutes, as a ball played into the back post was headed over.
Jordan Wright had to come on late on to replace the injured Griffiths in goal for Lincoln, which will be a concern for The Imps going forwards.
Full time saw Lincoln secure a vital win in their fight for League One survival, but for Wednesday it was a poor performance which may prove costly as they fight for a playoff place.
Takeaways from the match
Lincoln were able to show the character they needed if they want to stay in Sky Bet League One on Saturday afternoon, taking an early lead, weathering the Wednesday storm and making the most of their chances.
The hosts managed to take their chances and did not allow Wednesday many significant chances, defending expertly throughout the game.
The Owls on the other hand were poor on the day, showing their inconsistency when it mattered, as they went into the game in fantastic form, only to pass up on the opportunity to pick up three more points.
It may be losses such such as this one against a struggling Lincoln side that cost Wednesday come the end of the season.
They were pegged back very early on in the game, and whilst their initial respsonse to going behind was good, they were shaky in defence and had plenty of chances to score more than just the one goal.
They were silenced going forwards by the hosts especially well after the interval too.
Two goals and an assist for John Marquis made him the easy pick for the stand-out player from the game.
He caused all sorts of problems for Wednesday all afternoon, as he was powerful and clinical with his shooting.
The English striker was able to find pockets of space on the pitch and exploit the time he had afforded himself.
He scored a poacher's effort early on, set the ball back to Norton-Cuffy for him to score and scored a wonderful drilled shot to seal the win for Lincoln.
Lincoln City: Griffiths (Wright 90'), Poole, Whittaker, Hopper, Maguire, Walsh, McGrandles, Fiorini, Norton-Cuffy, Eyoma, Marquis.
Sheffield Wednesday: Peacock-Farrell, Palmer, Hutchinson, Bannan, Paterson (Kamberi 68'), Byers (Dele-Bashiru 75'), Johnson, Luongo, Berahino (Gregory 68'), Hunt, Storey.
Referee: Martin Coy.