A controversial Peter Thorne penalty denied administration-threatened Leeds a victory at Elland Road.
Peter Thorne scored his 11th goal of the season
David Healy and Gary Kelly went close for the home side, before 17-year-old Simon Walton took a return pass from Healy to drive in a superb goal.
But Leeds took their foot off the gas as Cardiff dominated the second half.
On 50 minutes, Richard Langley looked to have dived in the box, but referee Neale Barry gave a penalty, Peter Thorne calmly sliding in the spot kick.
Leeds manager Kevin Blackwell:
"I didn't think it was a penalty but I'm not going to condemn the referee because he has made his decision and we have to get on with it.
"I've not bothered speaking to him. If you say anything, you only get criticised or fined and right now I need all the money I can get for the mortgage.
"Over the two halves I think we deserved it, although the second half was much closer after being in total control in the first.
"But we showed our resilience to hang in there and get a result. Everybody has tried their hardest."
Cardiff manager Lennie Lawrence:
"After 20 minutes I'd have been delighted with a point, but at the end I wanted another 10 minutes and we'd have got the win - it was a moral victory for us.
"If things are going well for Leeds they knock it around and are difficult to cope with, but when they get forced back they are not so good.
"It looked like a clear-cut penalty to me. If it had happened in our box, I would have been looking away and praying we got away with it."
Leeds: Sullivan, Kelly, Butler, Kilgallon, Richardson,Walton (Spring 85), Wright, Pugh, Joachim, Healy,Lennon (Carlisle 57).
Subs Not Used: Carson, Ricketts, Griffit.
Goals: Walton 14.
Cardiff: Warner, Weston, Gabbidon, Collins, Barker, Langley,Inamoto (Ledley 88), Kavanagh, McAnuff, Thorne, Jerome (Lee 30).
Subs Not Used: Bullock, Vidmar, Alexander.
Goals: Thorne 52 pen.
Ref: N Barry (N Lincolnshire).