Aki Riihilahti, making his first start after a long lay-off, scored the only goal on 70 minutes to give the Eagles three vital points to consolidate their play-off spot.
A poor first half saw few incidents of note.
The Bluebirds were lucky not to concede a penalty on six minutes after Jobi McAnuff put Andy Johnson away and Cardiff defender Neil Cox seem to pull down the Eagles striker.
Referee Bates was barely over the halfway line to make the decision and Cardiff breathed a sight of relief.
On 15 minutes Dougie Freedman broke down the left side and crossed for McAnuff, who hit the underside of the bar before Michael Hughes slammed the rebound wide.
This apart the match lacked real penetration and indeed Cardiff failed to deliver one serious shot at goal. Although Cameron Jerome found the net but it was disallowed for a foul.
Jason Koumas had a good chance a few minutes before the break. Fitz Hall made a dreadful clearance allowing Kevin Cooper to cross to the far post.
Gabor Kiraly could only parry the ball to Koumas who wanted far too much time, and Emmerson Boyce did well to make the crucial block.
After the break Koumas forced Kiraly into his first, and what proved to be his only, save.
The match remained scrappy, although Freedman should have done better when he chose to shoot from an acute angle instead of pulling the ball back into the goalmouth.
The breakthrough for Palace eventually arrived on 70 minutes, after Johnson picked up the ball just outside the area and made a brilliant run, passing three defenders before pulling the ball back for Riihilahti to side-foot into the open goal.
Riccardo Scimeca headed over from a good chance before referee Bates, on the advice of his assistant, gave Hall his marching orders for an apparent elbow on Jerome.
Cardiff threw everyone forward, but despite some hard work their play lacked class and they failed to test Kiraly.