Cameron Dawson laid a foundation built upon by Anthony Musaba as the Owls posted a maiden away win of the season at Stoke.
Dawson saved Ryan Mmaee’s penalty in the second half before Musaba came off the bench to fire a late, late winner right in front of the travelling hordes.
Earlier on a cold afternoon in Staffordshire, there was little sign of the drama to come.
Neither goalkeeper was tested throughout a low-key first half. The closest Wednesday came was Akin Famewo inches away from connecting with a Liam Palmer cross at the back post but that aside, the opening period matched the miserable weather conditions.
The second half was in real need of a winter warmer and George Byers almost provided it three minutes in.
Palmer crossed, Josh Windass laid off, and Byers swivelled to shoot on the angle only to see the ball crash against the outside of the upright.
That gave Stoke a jolt and the hosts responded with their first shot of the afternoon, skipper Josh Laurent sending a low drive from distance wide.
That was followed by Mehdi Leris forcing a good save from Dawson as some life was injected into the contest.
And on 64 minutes came the big talking point and what could have been the deciding factor for Stoke as they were awarded a contentious penalty.
Famewo tangled with Leris in the box and the referee pointed to the spot - Mmaee struck hard to the right of Dawson, who sprang across his line to parry.
And that set up the grandstand finish as Musaba had the final say.
Deep into stoppage time, the Dutchman raced clear one-on-one with Tommy Simkin and the shot was unerring to give Wednesday a vital three points.
Wednesday: Dawson, Palmer, Diaby, Bernard, Famewo (Ihiekwe 69), Vaulks, Byers (Smith 79) Bannan, Johnson, Windass (Gussama 79), Cadamarteri (Musaba 58)
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