A pulsating, ding-dong Championship clash ended with the Owls overturning a 2-0 deficit into a 3-2 win, with a decisive goal from Kieran Lee clinching an unlikely success.
Five goals, two red cards and a missed penalty punctuated a game that was earlier threatened by adverse weather conditions in S6.
A torrential pre-match downpour triggered a 15-minute delay to the kick-off, after which a cagey opening gave way to a Hillsborough thriller.
City hitman Tammy Abraham struck his sixth and seventh goals of the season in the first half but Steven Fletcher pulled one back straight after the break.
Sam Hutchinson and Gary O’Neil then each saw red within a minute and sandwiched in-between was a City spot-kick that Lee Tomlin smashed against the woodwork.
That gave Wednesday a huge lift and Barry Bannan fired a fearsome long-ranger past Richard O’Donnell before Lee struck in stoppage time to complete the comeback.
There were few signs of the drama to follow in the early stages as the Owls enjoyed more of the possession but the Robins had the edge in terms of chances – and they hit the hosts with a quick-fire brace from dangerman Abraham.
First, on 32 minutes, the Chelsea loanee headed an O’Neil cross into the roof of the net before doubling the lead seven minutes later, this time nodding in after Keiren Westwood saved spectacularly from O’Neil.
It was hard on a Wednesday side that pushed and probed, with only the final ball missing to penetrate a rigid visiting backline.
The approach play was there and kicking towards the Kop in the second half, the Owls needed a boost - and got exactly that on 62 minutes.
Just after Kieran Lee forced ex-Owl O’Donnell into a fine save, Fletcher headed home an accurate Fernando Forestieri corner to halve the deficit.
Then the game really exploded into life on the hour, with two red cards and a penalty inside three manic minutes.
Hutchinson was sent off for a foul in the box on Marlon Pack but Tomlin, given the chance to all but make the points safe, slammed his spot-kick against the post.
The Owls immediately went on the attack and when O’Neil scythed down the onrushing Gary Hooper, the red card came out again to reduce both sides to ten men.
Wednesday had the bit between their teeth and got their reward on 75 minutes when Bannan unleashed from distance and the ball flew into the top corner off the diving O’Donnell.
Fletcher and Forestieri went close but Lee went one better, finishing a fine move to drill across O’Donnell to send Wednesdayites home delirious.
Wednesday: Westwood, Hunt, Lees, Hutchinson (Hooper 63), Pudil (Forestieri 45), Bannan, Lee, Jones (Wallace 46), Reach, Hooper (Sasso 63), Fletcher