Bruno Manga’s first Cardiff goal and Federico Macheda’s strike put the Bluebirds in control.
Alex Mowatt gave Leeds hope by pulling one back 13 minutes from time, but Kenwyne Jones made the points safe when he pounced on a defensive mix up to slot home his sixth goal of the season.
Redfearn’s full-time appointment was confirmed prior to kick-off, with the 49-year-old handed an initial 12-month contract with an option for a further year or a return to his academy duties once that period is over.
He is already the third manager to take the helm of the Yorkshire club this season, and Leeds fans will hope he can have the sort of stabilising effect Slade has had at Cardiff.
Bluebirds fans will have some sympathy with the current plight of their Leeds counterparts given the headlines their club has had to endure under Vincent Tan’s ownership.
But they are back on track after three wins out of four under Slade, moving them to the brink of the play-off places.
While United showed no lack of fight, Cardiff had the better of the opening exchanges and rarely threatened to relinquish control.
As early as the 11th minute Marco Silvestri had to get down low to his left to keep out Peter Whittingham’s free-kick, with the keeper also clawing away Anthony Pilkington’s header from under his own bar.
The visitors should have led in the 20th minute, but their best chance of the game was spurned by Steve Morison.
The Wales striker powered a header over the bar from 10 yards out after being found by Stephen Warnock’s superb centre.
Souleymane Doukara struck an effort straight at David Marshall from distance, but the better opportunities were coming at the other end.
Adam Le Fondre twice failed to make the most of good deliveries from Whittingham, glancing two headers well wide of the target, while Macheda’s shot was well blocked by Guiseppe Bellusci after John Brayford had led a sharp Cardiff break.
The second half settled into the same pattern and it was no surprise when Cardiff took the lead.
Leeds failed to clear a cross and when Sean Morrison headed Craig Noone’s cross back across goal, Manga was there to direct the ball into the bottom corner.
Six minutes later and the points looked secure when Macheda drove forward and powered his third goal in four games into the top corner, with the help of a deflection off Jason Pearce’s boot.
But Leeds found a way back into the game when Doukara got away from Fabio and picked out Mowatt for the midfielder to fire an angled drive across Marshall.
However, any hope of a comeback was sunk when a mix-up between Silvestri and Bellusci allowed Jones a simple finish.