Sean Morrison had put the Bluebirds ahead only to bring the visitors level by putting through his own net early in the second half.
But Anthony Pilkington's excellent control and right-foot finish gave the Welsh club the spoils for the first time in seven games.
It also secured a first win at the helm for stand-in bosses Danny Gabbidon and Scott Young.
But it remains to be seen if they will take charge against Brighton on Tuesday as Cardiff work to agree a compensation package with Leyton Orient and appoint Slade as Ole Gunnar Solskjaer's successor.
Young had spoken frankly of his disgust at the midweek Capital One Cup humbling against Bournemouth, but the home side almost suffered another nightmare start.
After just five minutes Jacques Maghoma freed Stevie May, but the striker was denied by Fabio's superb covering block after rounding David Marshall.
The Owls had won four out of five on their travels before the trip to south Wales, and they enjoyed the better of the early going against a hesitant home side.
Cardiff slowly found their feet and it took a superb stop from Keiren Westwood to claw Aron Gunnarsson's header away, with Kenwyne Jones prodding the follow-up wide.
But there was no reprieve for Wednesday six minutes before the break. Joe Mattock's foul on Mats Daehli allowed Peter Whittingham to deliver a pin-point free-kick onto Morrison's head for the centre-half to open his Cardiff account.
Wednesday were furious when Fabio survived a penalty appeal for handball early in the second half, but they did not have to wait long as they levelled in the 48th minute.
Giles Coke's challenge allowed Chris Maguire to roll the ball into the six-yard box where Morrison could only steer the ball into the bottom corner of his own net.
Maguire thought he had created another Wednesday goal eight minutes later as May closed in at the far stick, but could not find the target.
At the other end Westwood saved from point-blank range to keep out a Pilkington volley from Daehli's excellent cross
The Cardiff pair were also involved in the winner. The Norwegian's cross was headed down by Jones for Pilkington to control and rifle a low right-footed shot beyond Westwood.
Young and Gabbidon decided the time was right to hand Ravel Morrison a debut, following his midweek loan move from West Ham, and the England Under-21 cap quickly showed his talents with a lovely drag-back which left two defenders standing.
He came close to setting up a third Cardiff goal, scooping out a cross from the byline that Pilkington could not connect cleanly with.
But it did not matter as Cardiff returned to winning ways.