Leeds started well, but on the stroke of half-time Michael Chopra fired Cardiff ahead with a 20-yard free-kick.
Chopra had already been booked when his 66th-minute challenge on Hayden Foxe earned a second yellow and sending off.
Steve Thompson missed a penalty for Cardiff after Tresor Kandol handled in the area, then Simon Walton was harshly sent off for his second yellow late on.
Leeds assistant manager Gus Poyet:
"We have missed a great chance of getting something from this game but when you are down there at the bottom something always seems to happen.
"Crucially they scored on the stroke of half time and after that we were always chasing the game.
"I think it was the best 30 minutes we have played away from home this season but when you are down there no-one will help you and we must pick ourselves up for the next match."
Cardiff: Alexander, Gilbert (Gunter 46), Ledley, Johnson, Walton, McNaughton, Whittingham, McPhail, Parry, Chopra, Thompson (Byrne 89).
Subs Not Used: Flood, Forde, Redan.
Sent Off: Chopra (66), Walton (84).
Booked: Thompson, Chopra, Walton.
Goals: Chopra 45.
Leeds: Ankergren, Armando Sa, Rui Marques (Foxe 41), Heath, Douglas, Westlake (Cresswell 60), Lewis, Nicholls, Moore, Kandol, Blake (Healy 60).
Subs Not Used: Stack, Howson.
Booked: Foxe, Kandol, Nicholls.
Ref: M Clattenburg (Co Durham).