The visitors were the better side for much of a dour first half but fell behind when Angus MacDonald put the ball past his own goalkeeper.
Wednesday came out with renewed belief in the second period as they began to play with more purpose, but Barnsley continued to pose problems and it was only when Sam Hutchinson fired home with 10 minutes remaining that the result was put beyond doubt.
Hutchinson was then involved in an incident that saw Barnsley substitute Adam Hammill and manager Paul Heckingbottom sent off as a fiery second period provided a stark contrast to the first 45 minutes.
For a local derby the game began at a sluggish pace, with Wednesday left-back Daniel Pudil blasting high and wide in the second minute.
Conor Hourihane was similarly off-target for the visitors from 20 yards after a well-worked free-kick routine, while keeper Keiren Westwood rushed out well to deny Tom Bradshaw after some woeful defending saw the Barnsley forward race clear.
Steven Fletcher headed an Adam Reach corner wide and then wriggled clear in the box after 36 minutes but dithered over his shot and the opportunity passed.
It did not matter, however, as a minute later a suitably scruffy goal gave the home side the breakthrough.
Lucas Joao out-jumped the Barnsley defence and his flick was inadvertently turned into his own net by MacDonald.
Bradshaw wasted his second glorious opportunity of the game five minutes after half-time when he headed over Ryan Kent’s free-kick from six yards.
Sam Morsy’s shot was blocked after good work from Sam Winnall and Kent as the away side started the second period impressively.
The home side responded, with substitute Ross Wallace playing in Reach, whose cut-back was hacked away for a corner, before Fletcher failed to trouble Adam Davies with a header from Pudil’s searching pass.
Barry Bannan tested Davies from the edge of the box on the hour mark, but the visiting keeper was equal to it, before Fletcher and Liam Palmer contrived not to score after Reach’s excellent work down the left.
Winnall’s miscued effort after 63 minutes fell kindly for Bradshaw, but the Welshman’s effort lacked the power to beat Westwood.
Tom Lees should have put the game to bed with 20 minutes remaining but fired wide from Wallace’s corner when the ball fell to him six yards out.
The lively Kent fired high and wide at the other end as he snatched at James Bree’s cross, but Hutchinson converted from 12 yards following a Wallace corner to double Wednesday’s lead.
Barnsley sub Hammill was then sent off for a challenge on Hutchinson that sparked brawls both on the pitch and the touchline, with visiting boss Heckingbottom sent to the stands.
Kieran Lee could have made it three late on but he narrowly failed to connect with Fletcher’s header back across goal.