Glenn Murray thought he had given the Seagulls the lead in the 79th minute, but the goal was disallowed after referee Roger East pulled play back for a foul.
The result means that Brighton close the gap to just a point to league leaders Newcastle, and remain unbeaten since September. Meanwhile, Cardiff stay in the bottom three.
Cardiff fired the first warning sign when Iceland star Aron Gunnarsson weaved his way to the edge of the box and saw his shot saved by David Stockdale.
The Bluebirds nearly gifted Brighton a goal in the 13th minute after Sam Baldock dispossessed Joe Bennett in the box, who squared the ball to Murray, but the forward failed to connect.
In a quiet first half, Jiri Skalak’s free-kick from 20 yards out hit the wall, but when it came back to him, his ferocious drive went just wide of Ben Amos’ goal.
Cardiff started the second half well and could have been ahead when Sol Bamba headed wide from just three yards out, following an inviting Joe Ralls cross.
And with chances few and far between Baldock wasted a golden opportunity for the away side after skewing Skalak’s cut-back horribly wide.
Brighton applied the pressure in the latter stages of the game when Matthew Connolly excellently blocked Murray’s goal-bound effort.
Baldock’s smart turn in the box allowed him to get a shot away and force Amos into a good save in the 82nd minute.
Brighton had to play out injury-time with 10 men as Gaetan Bong picked up a second yellow card after a cynical trip on Kadeem Harris.
Despite remaining in the drop zone, Cardiff will be happy with a first clean sheet in 18 games.