City, whose slim hopes of a play-off spot ended in midweek with Brentford's win at Wrexham, tore Wednesday to shreds in the opening minutes with skipper Steve Brooker scoring twice.
Wednesday hit back with two quick goals before keeper Paul Gallacher was red carded after colliding with Brooker as Luke Wilkshire tucked away the spot-kick.
Gallacher was busy in the opening minutes. He saved bravely at the feet of Paul Heffernan before Brooker beat his marker to Wilkshire's free-kick but headed over from six yards.
Heffernan had the best opportunity after a mistake by midfielder Chris Brunt but fired wide from 15 yards.
Heffernan was involved again in the 15th minute as he latched on to defender Lee Bullan's mistake but was foiled by Gallacher as the keeper charged off his line to sweep the ball away.
City edged ahead in the 25th minute with the help of keeper Steve Phillips' long kick and the strong wind which swept the ball into the Wednesday area. Bullen and Gallacher both misjudged the kick as Brooker nipped in to prod the ball home from eight yards.
City almost grabbed a second in the 40th minute, Brooker twisting past Bullen to fire in a low drive smothered at the foot of the near post by Gallacher.
Under-pressure Wednesday set up their only chance of the half a minute later, midfielder Glenn Whelan squandering it as he hammered Andrew Talbot's precise cross over the target.
Brooker struck again with a spectacular strike on 44 minutes as he worked his way across the face of the goal before hammering in a right-foot strike from 16 yards.
Luck was on Wednesday's side in the 52nd minute when Whelan's mis-hit shot fell straight at feet of the unmarked John Paul McGovern who beat Phillips from 10 yards.
Richard Wood struck nine minutes later heading in Paul Heckingbottom's free-kick.
Louis Carey hit a post in the 68th minute with a piledriver from 25 yards before Brooker chased another long ball downfield and collided with Gallacher as he came off his line.
Gallacher was sent off as substitute Lee Peacock, on at half time for James Quinn, took over in goal but was beaten by Wilkshire's spot-kick.