Wednesday debutant John Bostock, signed on loan from Tottenham, went close with a free-kick which only just cleared the bar. Then Jermaine Johnson posed a threat to the visitors with a shot from just outside the area which went wide.
Jonathan Obika gave Yeovil a 41st minute lead, poking the ball past Stephen Bywater following an incisive through ball from Ryan Dickson.
Andrew Williams threatened to put the visitors further ahead before the break when his low angled shot went narrowly wide.
In the 57th minute Jermaine Johnson struck a superb equaliser, finding the net from around 30 yards.
The home side continued to press after the goal with Reda Johnson, Chris O'Grady and Ryan Lowe all putting efforts off-target. And it was no surprise when Wednesday grabbed an 80th minute winner, Reda Johnson following up to fire home after Clinton Morrison's effort was saved by Sam Walker.