Scott Wiseman's cross created a simple tap-in for Matt Done in the 15th minute and Daniel Jones' foul on Done 12 minutes later handed Rochdale a penalty, converted by skipper Gary Jones, while Wednesday replied through striker Gary Madine in the last minute.
The result made it 10 games unbeaten for Keith Hill's men with the Owls falling to their first defeat under new boss Gary Megson.
Wednesday's Giles Coke had a shot blocked on the line by Chris O'Grady minutes into the second half, while Lewis Buxton's cross found Gary Madine free in the area, but the Owls striker was unable to bring the ball under control.
But Rochdale were relatively comfortable and could have had a third when Done drifted between two defenders on halfway to race through on goal, only for visiting goalkeeper Nicky Weaver getting the better of their one-on-one.
Fon Williams got his fingertips to a fierce drive by Isiah Osbourne late on, but was powerless when Madine headed home Buxton's cross in the 90th minute.