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.
From Craig Bellamy's subsequent corner, Chris Kirkland fumbled the ball under pressure but was awarded a fortunate free-kick for some shoving in the area.
Leroy Lita took a tumble in the penalty area to loud appeals from the home fans, but the challenge from Leon Barnett was deemed a fair one by referee James Linington.
Lita and Linington took centre stage again moments later when Cowie fell to the ground holding his face, with his team-mates claiming Lita had aimed an elbow at him.
After allowing play to go on, the official returned to the incident and decided no further action was be necessary.
Midway through the half Barnett sloppily conceded possession 20 yards from goal, but Michail Antonio failed to make the most of it as his tame shot was easily blocked away.
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 Kirkland's net.
It was a bitter pill for Jones and his charges to swallow and they were almost caught napping early in the second half when Heidar Helguson looked to play Campbell in, but Llera was alert to the danger and slid in brilliantly to thwart the striker.
There was no-one to save the hosts in the 65th minute when 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.
Lita had an effort ruled out for offside and the visitors survived a goalmouth scramble late on, with just enough time left for Bellamy to endear himself to the home fans by going in the book for a crunching challenge on Johnson.