Caulker, who was part of Roy Hodgson's England squad in midweek, concluded a listless first half with a close-range finish in stoppage time.
Fulham responded well and levelled before the hour through Lewis Holtby but Caulker headed a second and an unfortunate own goal by Sascha Riether completed the visitors' misery.
Ole Gunnar Solskjaer's Cardiff are now only below fourth-bottom West Brom on goal difference, while Fulham remain bottom with 16 losses from their last 21 league outings.
Felix 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.
Fulham benefited from a 10th-minute opening as John Heitinga's quick free-kick caught the Cardiff defence napping, but Ashkan Dejagah fired wastefully into the side-netting from a tight angle with Mitroglou well-placed centrally.
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 keeper some far more taxing work - a stunning reflex save thwarting Jones from close quarters.
Unfortunately for Fulham, they failed to effectively clear from the corners that followed and when Craig Noone's low cross was deflected across the six-yard box Caulker was left with a tap-in.
Magath's men made a livelier start to the second period, Holtby testing David Marshall in the Cardiff goal from Woodrow's knockdown, but Jones should have doubled the hosts' lead in the 50th minute as he headed wide at the back post on the end of a searching Noone cross.
Cardiff sealed the points in scrappy fashion as another excellent Noone cross was bundled goalwards by Campbell. Stekelenburg's point-blank stop was impressive but the loose ball cannoned into Riether and trickled over the line.
