Two quickfire goals in the second half cancelled out Atdhe Nuhiu's late header to give Swansea victory over the Owls at the Liberty Stadium.
Wednesday failed to take advantage of first half dominance that spawned a host of chances, leaving the Swans to snatch all three points courtesy of Rhian Brewster and Andre Ayew.
Nuhiu nodded home in the final minute of the game, but there wasn't enough time left on the clock for Wednesday to mount a charge for an equaliser.
It was hard on Garry Monk’s men, who took the game to their hosts and should have been in the driving seat at half time.
But it was a familiar story in South Wales, marking an unhappy return to Swansea for ex-boss Garry Monk.
After a relatively uneventful opening, his side carved the first opportunity on the 15-minute mark.
Adam Reach darted to the byline and delivered across the face of goal to Jacob Murphy at the back stick but the wideman’s shot was way too high on the half volley.
Murphy did find the target moments later to warm the gloves of Freddie Woodman as the Owls bossed the ball and looked far the more threatening.
Swansea struggled to make any kind of impact in the final third, with the Wednesday backline well organised in the revised 3-5-2 formation.
That gave the visitors the foundation on which to pour forward and again they came close 10 minutes before the break.
A mini scramble in the area led to Alessio Da Cruz taking aim and his low effort was well struck, only for Marc Guehi to divert almost on the goal line.
But Wednesday had their best chance right on the half time whistle – Barry Bannan crossed deep to Da Cruz, the Dutchman’s header sailed over the bar and Swansea considered themselves fortunate to head down the tunnel on level terms.
And the hosts certainly capitalised, taking the lead with their first attack of purpose six minutes into the resumption.
After Joe Wildsmith kept out Ayew’s set piece, the ball was back in the box from the resulting corner and Brewster eventually pounced with a fierce drive that slammed into the back of the net.
The Owls regrouped and headed back upfield – Dominic Iorfa was a whisker way from converting Murphy’s driven feed on the hour.
But Wednesday’s luck was out and they went further behind on 66 minutes from the spot.
Reach tangled with Connor Roberts from a looping cross, the referee saw an infringement and leading scorer Ayew sent Wildsmith the wrong way from 12 yards.
From a seemingly strong position, the Owls suddenly found themselves 2-0 down and chasing the game.
The Swans, though, gained a new-found confidence from their two-goal salvo and Wednesday found it hard to force a way through.
And it was the home side who should have put the points to bed with eight minutes to go but Brewster screwed wide advancing on goal on the angle.
Substitute Nuhiu pulled a close range shot across Woodman and wide in the next passage of play, but his final attempt would be more clinical.
Murphy crossed from the right and the Kosovan striker's clean header was too powerful for Woodman, but it proved to be just a consolation for the Owls.
Wednesday: Wildsmith, Iorfa, Börner, Palmer, Murphy, Bannan, Reach (Harris 67), Luongo (Nuhiu 70), Lee (Hunt 46), Da Cruz (Rhodes 79), Wickham