Goals from James O'Connor and Darren Potter gave the Hillsborough side their fifth win from seven games since the ex-Preston boss took over.
Wednesday got off to a dream start after scoring with their first attack on three minutes.
Full-back Tommy Spurr pumped over a precise cross from the left and midfielder O'Connor rose unmarked to head firmly past Paul Rachubka from six yards.
The Sheffield side escaped minutes later when Keith Southern was allowed a free route into the area but, as three defenders backed off, the Blackpool midfielder lost his footing and his left-foot shot flew high and wide.
Jason Euell almost found a way through after Lee Grant failed to hold onto David Vaughan's looping cross but, with the lanky midfielder about to pounce, the Wednesday keeper smothered the ball at his feet.
They were in trouble again in the 31st minute when Stephen Dobbie picked out Dudley Campbell but the little striker pulled his close-range header wide of the target.
Wednesday, who were lucky to cling onto their slender lead in the opening period, stepped up the pace after the break.
Potter almost added a second as he ran onto Luke Varney's measured pass but his strike from 25 yards took a deflection and the ball spun inches wide.
The lanky midfielder had better luck in the 50th minute with Varney again the provider as Potter cleverly curled the ball beyond the diving Rachubka into the bottom left-hand corner.
Varney almost grabbed a third as the Sheffield side took a stranglehold on the game.
Tom Soares fed the in-form striker, whose shot from 15 yards was turned around the post by Rachubka.