Steven Caulker scored twice as Sascha Riether's own goal wrapped up the points for Ole Gunnar Solksjaer's side, which has closed in on West Brom in 17th place.
Steven Caulker opened the scoring from close range just before halftime, but Felix Magath made two changes and saw Lewis Holtby equalize after the break.
|VIEW FROM CARDIFF CITY STADIUM
|By Jamie Dunn
Felix Magath insisted the pressure was on Cardiff ahead of his side's trip to Wales — but after this dismal 3-1 defeat there is no doubt that Fulham is in serious trouble.
Magath started Kostas Mitroglou and debutant Cauley Woodrow, but neither could spark Fulham into life. After a poor start to the game, Cardiff went in front through Steven Caulker.
The German responded, making two changes, and second-half substitute Giorgos Karagounis played a part in Lewis Holtby's equalizer.
But Cardiff was simply the better side and deserved this win. Led by Jordon Mutch and the increasingly impressive Craig Noone, Caulker scored again when Maarten Stekelenburg could have done more to keep him out, before Sascha Riether's own goal summed up the afternoon for the visitors.
Ole Gunnar Solskjaer's Cardiff is now only below fourth-bottom West Brom on goal difference, while Fulham remains bottom with 16 losses from its last 21 league outings.
Magath handed a first Premier League start to Kostas Mitroglou but the most eye-catching selection came alongside Fulham's record signing in attack, with 19-year-old Cauley Woodrow given a surprise debut.
John Heitinga's quick free kick caught the Cardiff defense napping early, but Ashkan Dejagah fired wastefully into the side-netting from a tight angle with Mitroglou well-placed centrally.
Visiting goalkeeper Stekelenburg punched to safety in the 16th minute after Fraizer Campbell shimmied past a pair of challenges to unleash a venomous strike.
Kenwyne Jones headed into Stekelenburg's arms from a Jordon Mutch cross and the duo combined again in the 44th minute to offer the former Ajax goalkeeper some far more taxing work — a stunning reflex save thwarting Jones from close quarters.
Unfortunately for Fulham, it failed to effectively clear from the corners that followed and when Craig Noone's low cross was deflected across the 6-yard box, Caulker was left with a tap-in.
Magath brought on Alex Kacaniklic for for John Arne Riise at halftime and Giorgos Karagounis for Dejagah shortly after.
And the resulting pressure told in the 59th minute when an inswinging corner from Karagounis was flicked on by Heitinga at the near post for Holtby to convert.
The set-piece defending from both teams showed scant sign of improving and Stekelenburg was forced into another fine stop as Kim Bo-Kyung fired through a crowded penalty area.
Stekelenburg should have completed an arguably easier save from another corner but he could not keep the ball out when Caulker rose unmarked to head his second.
Cardiff sealed the points in scrappy fashion as another excellent Noone cross was bundled goalward by Campbell. Stekelenburg's point-blank stop was impressive but the loose ball cannoned into Riether and trickled over the line.
Mitroglou forced an excellent save out of Marshall in the 77th minute, while Steve Sidwell saw a late header ruled out for offside as Cardiff moved up the table.