Stephen Crainey's foul on Joel McAnuff gave the home side a 19th-minute spot kick, but Sullivan saved Andy Campbell's shot with his feet.
The hapless Campbell hit the post from close range in the second half before being substituted.
McAnuff hit the bar with a 25-yarder, but Sullivan had the final word, tipping Peter Thorne's snap-shot away.
Leeds boss Kevin Blackwell:
"It was a hard-earned point. Lennie Lawrence had his players up for the game and I am pleased with the clean sheet.
"I felt the penalty decision was shoddy and justice was done when Neil saved it.
"I knew how big a game it was for both sets of fans and we were very lucky when they struck our woodwork three times.
"I was told by Cardiff defender Robert Page that this was the best they have played all season but that doesn't surprise me - everyone lifts their game against us."
Cardiff: Warner, Vidmar, Gabbidon, Williams, Barker, McAnuff,
Boland, O'Neil, Parry, Campbell (Jerome 70), Thorne.
Subs Not Used: Robinson, Collins, Bullock, Alexander.
Leeds: Sullivan, Kelly, Carlisle, Butler, Crainey,
Richardson (Joachim 61), Wright, Gregan, Pugh, Ormerod,
Deane (Ricketts 64).
Subs Not Used: Carson, Spring, Duberry.
Booked: Gregan, Wright.
Att: 17,006.
Ref: P Crossley (Kent).