It had been a poor encounter which Barnsley had dominated until Gary Madine ended a four-month wait for a goal when he finished from close range in the 65th minute.
That goal inspired Wednesday and Reda Johnson made it two with a header 12 minutes later and Madine should have put the gloss on it but he missed from the spot before Lewis Buxton saw red following two yellow cards.
However, with results elsewhere going against them, the Owls were unable to put further distance between themselves and the bottom three, meaning their quest for survival looks like going down to the wire.
Barnsley's fate will also not be decided for a few weeks as this defeat, which rarely looked on the cards until the Owls' opener, ends a sequence of back-to-back wins and sees them drop back into the bottom three, despite Jacob Mellis' late consolation.
The opening exchanges lacked the intensity you would expect from a South Yorkshire derby that had huge importance at the bottom of the league, though Barnsley had the better of the first 15 minutes, with Jim O'Brien dragging an effort wide and Chris Dagnall seeing his shot spilled by Chris Kirkland.
After a lengthy period of poor quality play there was finally some goalmouth action to savour shortly before the break as Dagnall's shot was well blocked by Miguel Llera and then Marlon Harewood hooked wide from a good position at the far post following a good cross from Tom Kennedy.
Having had no shots on target in the first half, Wednesday could not be any worse after the break and they did force Steele into some work, first from Leroy Lita's tame header and then from a Reda Johnson header, which the defender should have done better with.
Those two efforts did little to spark the Owls into life, though, as the Reds continued to be the better side and they almost broke the deadlock on the hour. David Perkins found Reuben Noble-Lazarus and the substitute unleashed a vicious effort that Kirkland superbly turned over the bar.
David Flitcroft's men continued to push and Kirkland was again called into action when he got down well to keep out Jason Scotland's effort after the impressive Mellis burst into the box.
Just as it looked like Barnsley were edging ahead, Wednesday took the lead out of nowhere and against the run of play. Lewis Buxton broke down the right after Jermaine Johnson's pass and slid a superb ball across the face of goal which Madine turned in at the far post. Madine had been a virtual spectator until his timely contribution and it was his first goal since early December, a run of 13 games.
The deserved second eventually came in the 77th minute when Reda Johnson had acres of space to head home Llera's free-kick. It was all Wednesday at this point and it should have been three but Madine blazed his spot-kick wide after Bobby Hassell's handball.
However, Barnsley made a game of it in six minutes of added time when Mellis smashed home from 16 yards as a previously drab game ended in a flourish.