Steve Morison went close for Redfearn's side when he connected with Stephen Warnock's cross, but the ex-Reading striker's header flew just wide after 20 minutes.
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Souleymane Doukara fired in an effort for Leeds on the half-hour mark but his strike was comfortably held by David Marshall.
Le Fondre was again culpable of another miss with his head towards the end of the half when he glanced Whittingham's cross wide of the post.
However, the home side netted twice in six minutes after the hour mark and it was Gabon international Ecuele Manga who opened the scoring with a powerful header.
Former Manchester United striker Macheda doubled the advantage when his 25-yard strike took a deflection to fool Marco Silvestri in the Leeds goal.
Mowatt gave the visitors hope when he steered home after good work from Doukara, but a defensive mix-up saw Cardiff regain their two-goal advantage late on.
Silvestri raced off his line and collided with Giuseppe Bellusci to leave Jones with the easy task of knocking the ball into the empty net.