Luke Chambers’ header four minutes from time gave Town the points at Hillsborough after Tom Lawrence had scored his first goal for the Club.
The Blues’ skipper diverted the ball in after Christophe Berra had been first to Grant Ward’s free-kick.
Lawrence gave Town the lead just past the half hour with a terrific strike but Blues’ lead lasted only three minutes with Gary Hooper forcing the ball in from close range.
Jonny Williams went close for Town but the game seemed on course for a fifth successive 1-1 draw until the skipper took centre stage.
Town made one change to the side that drew with Rotherham last weekend, Jonas Knudsen returning after a back injury to replace Myles Kenlock.
Berra did well to stop Adam Reach getting in on goal inside the first two minutes, Blues responding on the break with David McGoldrick cutting inside and sending a left footer wide from 18 yards.
Barry Bannan rifled a strike wide after he had initiated the move with a burst from midfield, Freddie Sears then seeing a cross cleared after Ward had found him down the right in a bright start to the game.
Knudsen cleared after Steven Fletcher fed the ball back into the box, the Scotland international then having a shot deflected wide. From the corner, Fletcher headed over from close range in a gilt-edged chance.
Sears forced a corner with a terrific cross following Cole Skuse’s clever pass before Town got the breakthrough on 32 minutes, Lawrence winning the ball down the left and surging into the Wednesday danger area before firing into the bottom corner.
Bannan almost found Jack Hunt with a superb 50 yard pass as Wednesday looked to bounce back immediately and that’s exactly what the Owls did three minutes after Town’s goal, Hooper in the right place to fire in the rebound after Bart Bialkowski had saved from David Jones.
Lawrence had a free-kick beaten out by the Wednesday wall, Bialkowski off his line as Bannan again sent a testing long pass into Town territory with Reach heading wide at the far post in the last opening of the first-half.
It took a brilliant save from Bialkowski to prevent Hooper from putting Wednesday in front inside the first minute of the restart, Kieran Lee sending the rebound wide.
Fletcher headed wide after finding space at the far post, Wednesday then introducing Fernando Forestieri for Reach before the hour.
McGoldrick almost found Knudsen with a clever ball, Adam Webster showing his promise with a superb run from deep that was ended on the edge of the Wednesday box by Tom Lees’ challenge.
Williams replaced Bishop for the last 20 minutes, Bannan hounded out as he weaved his way into the Town box, David Jones then firing over from 25 yards.
Kevin Bru entered the fray, Lawrence making way. Sears was denied by Keiren Westwood after Ward released him in the box, Ross Wallace then seeing a cross deflected into the sidenetting.
Williams was denied from close range from Ward’s cross as Town threatened a winner and it came on 86 minutes, Ward’s free-kick was met by Berra and Chambers diverted the ball in.
Sheff Wed: Westwood, Jones (Wallace 74), Lee, Fletcher, Reach (Forestieri 56), Hooper (Abdi 80), Lees, Hutchinson, Hunt, Pudil, Bannan. Subs not used: Dawson, Loovens, Palmer, Buckley. Booked: Fletcher.
Town: Bialkowski, Chambers, Webster, Berra, Knudsen, Ward (Varney 88), Skuse, Bishop (Williams 69), Lawrence (Bru 78), Sears, McGoldrick. Subs not used: Gerken, Emmanuel, Kenlock, Best. Booked: Chambers, Ward.