Don Cowie's first goal since September on the stroke of half-time and Matthew Connolly's second-half header proved the difference as the visitors ended a three-match winless run that had threatened to derail their automatic promotion hopes.
The Owls continue to look nervously over their shoulders at the bottom three after a second home defeat in a row and third in four matches overall.
It was Wednesday, under the guidance of a man who led the visitors to two play-off campaigns and an FA Cup final in his six years at the helm, who started the brighter.
Jeremy Helan cut inside and fired in a low shot from the edge of the area which David Marshall clutched.
At the other end, Fraizer Campbell's menacing run into the box forced a timely block out of Miguel Llera.
Just as it looked as though it would be honours even at the break, Malky Mackay's side broke the deadlock.
The hosts failed to properly clear a corner and Cowie seized on the loose ball, struck his shot low and got a fortunate deflection off Anthony Gardner as the ball skidded into the back of Chris Kirkland's net.
In the 65th minute Peter Whittingham, making his 300th Cardiff appearance, arrowed in a free-kick from deep which Connolly nodded in from six yards for his fifth of the season.
Llera saw a curling free-kick tipped over the bar by Marshall three minutes later as Wednesday searched for a way back, but there was none.