Leeds came from behind to leave the Owls disappointed in the Hillsborough finale for the current campaign.
Steve Morison struck after Charlie Taylor cancelled out a Chris Maguire penalty, bringing the Whites’ five-game losing run to an end.
For Wednesday, the contest summed up their indifferent season on home soil as they rarely troubled Stuart Taylor between the sticks.
Leeds edged possession and chances, the first of which was as early as the opening minute when Alex Mowatt brought the best out of Keiren Westwood on the angle.
But the Owls found their stride and Caolan Lavery curled just over the bar following a dominant passage of play by the hosts.
Leeds, though, did look dangerous on the counter, as was evidenced by a Mowatt set piece on the 15-minute mark.
And from then on in for the first half, the Whites grew into the game and asked more of the questions.
Bu that was until the 35th minute when Wednesday broke themselves and won a penalty.
Sam Byram tripped Lloyd Isgrove just inside the area, the referee pointed to the spot and Maguire sent Taylor the wrong way from 12 yards.
The goal gave the Owls a visible lift and former Leeds defender Tom Lees almost raised the roof two minutes before half time with a looping header that Taylor tipped over the crossbar.
The second period continued on a similar balanced theme, with the Whites arguably just on top, and they duly equalised on 58 minutes.
A Luke Murphy free kick found its way to the loitering Taylor, who buried confidently past Westwood from close range.
That triggered a double substitution for Wednesday, with Stuart Gray introducing Stevie May and Will Keane from the bench.
But although the Owls began to edge more of the play, it was Leeds that struck the decisive blow on 72 minutes.
Leeds broke down the right through Morison, whose first shot was blocked by Westwood only for the striker to tuck away the rebound.
Owls: Westwood, Buxton, Semedo, Maguire, Lavery, Lees, Helan (Bus 85), Maghoma (May 64), Lee, Isgrove (Keane 64), Vermijl
Leeds: Turner, Byram, Bamba, Austin, Murphy, Berardi, Wootton, Morison, Taylor, Mowatt (Sharp 71), Cooper