Two goals from Steven Caulker and an unfortunate own goal from Sascha Riether were enough to give Ole Gunnar Solskjaer's side all three points, with Lewis Holtby briefly drawing Fulham level in the second half.
The win moves Cardiff level on points with West Brom, while Fulham remain rooted to the bottom of the table with just nine games left in the campaign.
After a nervy start from both sides, Fulham fashioned the first opening as Johnny Heitinga found Ashkan Dejagah with a quickly-taken free-kick, but the midfielder fired his shot into the side netting.
Five minutes later, Fraizer Campbell went close for Cardiff when he cut in from the left and beat a couple of Fulham defenders on the edge of the box before firing in a shot which forced Maarten Stekelenburg to push away at full stretch.
The lively Craig Noone created a chance for himself on 21 minutes when he skipped past Steve Sidwell and Brede Hangeland and shot narrowly wide of the post from the edge of the box.
The home side were on top and Kenwyne Jones headed straight at Stekelenburg from Jordon Mutch's cross before Noone drove a shot from 25 yards out over the top.
Fulham's record signing Kostas Mitroglou had a half chance on 40 minutes when Holtby picked him out inside the box, but the Greek striker got his header all wrong and it flew well wide of the target.
Cardiff went close to scoring on the stroke of half-time when Mutch's cross found Jones inside the box and his shot was well saved by Stekelenburg.
There was still time left for Cardiff to break the deadlock deep into injury time at the end of the first half as Fulham failed to clear their lines and Noone fired in a shot which deflected into the path of the grateful Caulker to convert two yards from goal, much to the relief of the home fans.
Fulham went close to equalising two minutes into the second half when substitute Alex Kacaniklic teed up Holtby on the edge of the box and his half-volley was superbly pushed away by David Marshall.
A minute later, Jones really should have doubled Cardiff's lead when Noone's deep cross found him unmarked at the far post, but the Trinidad and Tobago striker headed wide of the target with the goal at his mercy.
Jones and Cardiff were made to pay for that miss just before the hour mark when Heitinga flicked on substitute Giorgos Karagounis' corner and Holtby was left unmarked to tap home from close range with his first goal for Fulham since joining on loan from Tottenham in January.
Cardiff responded well to Fulham's equaliser and Kim Bo-kyung was unlucky not to score when his shot from inside the box was kept out by the legs of Stekelenburg.
From the resulting corner, Cardiff hit the front again as Caulker rose highest to meet Mutch's cross and his header bounced into the ground and somehow Stekelenburg dived under the ball to concede a soft goal.
Cardiff made it 3-1 on 71 minutes when Noone fired over another inviting cross from the right and Mutch saw his point-blank header saved by the feet of Stekelenburg, only for the ball to rebound off the helpless Riether and into the net.
Fulham tried to find a way back into the game and Mitroglou went close to scoring his first goal for the club, only to be denied by a flying save from Marshall before Sidwell had a goal disallowed for offside late on.
Cardiff saw out the closing stages with ease as they gave their survival hopes a major boost with a morale-boosting win to leave Fulham staring down the barrel of relegation.