Wednesday snatched the points through Chris Maguire despite having Jermaine Johnson sent off, as Barnsley finished with nine men after debutant Emmanuel Frimpong and Jacob Mellis were sent off.
Maguire was able to drill home from the edge of the area in stoppage time to give Wednesday the victory.
Frimpong's reckless challenge after just 31 minutes earned him a second yellow card to leave the visitors on the back-foot.
Owls substitute Johnson was then shown a straight red card after only 10 minutes on the pitch for a high challenge on Brek Shea.
Mellis was also shown a red card when he dived in on winger Jacques Maghoma before Maguire netted the winner.
Wednesday started the brighter of the two teams but Miguel Llera was unable to divert Maguire's teasing cross into an empty goal.
The Owls backline was then tested again when a corner routine left Reds defender Martin Cranie the space to fire at goal where Chris Kirkland acrobatically saved.
Llera was again unable to meet a cross as Maghoma's inswinging cross bypassed everyone.
Barnsley had to reshuffle after Frimpong's debut was cut short, with Chris O'Grady making way for young midfielder Stephen Dawson.
Atdhe Nuhiu had the chance to make the break-through but his header failed to hit the target after a Maguire cross.
Seconds before the interval the 10 men of Barnsley countered at pace with Dale Jennings forcing Kirkland into a fine save at the near post.
Jennings thought he had scored in the second half but his strike was ruled out for offside.
When Owls full-back Liam Palmer dispossessed Tom Kennedy on the hour-mark, Maguire was free to shoot but his effort was blocked.
American international Oguchi Onyewu then forced Luke Steele to tip over his crossbar following a Maguire corner.
Barnsley's woodwork was rattled from the resulting corner as Jack Hunt deflected Maguire's corner onto his own post.
Referee Andre Marriner then waved away a penalty appeal as substitute Caolan Lavery tumbled to the floor after a clash of legs between himself and Barnsley defender Peter Ramage.
Kieran Lee took aim from 20 yards and saw his deflected shot spectacularly saved by Steele who palmed the midfielder's effort wide of the post.
Substitute Johnson's late challenge on Barnsley's Shea levelled the sides up as he was shown a straight red card just ten minutes after coming on.
Mellis of Barnsley then made it three red cards in the 88th minute after sliding in on Maghoma, before Maguire fired home from 20 yards to give the Owls the three points.