On-loan Chelsea forward Gael Kakuta poked home his first goal in English football in the 33rd minute to give the visitors the lead before a Simon Davies double in the second half settled matters at the Stadium of Light.
Sunderland enjoyed much the better of the first half but failed to convert a number of decent opportunities and were left to contemplate an eighth defeat from 10 matches.
The hosts' ongoing injury crisis robbed them of any fit strikers, with Danny Welbeck and Asamoah Gyan both expected to miss the rest of the season after damaging hamstrings in last weekend's 4-2 win over Wigan.
That result allayed the Black Cats' relegation fears but had either Welbeck or Gyan been fit they surely would have converted at least one of the host of chances the home side created in the first half.
Sunderland dominated possession from the off and full-back Ahmed Elmohamady had the first decent chance in the 14th minute with a header glanced just wide from Phil Bardsley's cross.
The Fulham team featured three changes from Wednesday's 3-0 win over Bolton, the most notable of which was a debut for Philippe Senderos 11 months after he joined the club from Arsenal following his recovery from an Achilles injury.
Kakuta and Bobby Zamora also came into the side, with Brede Hangeland and Clint Dempsey left out altogether while Moussa Dembele dropped to the bench.
Eidur Gudjohnsen shot over in a rare chance for the visitors before Sunderland's wastefulness continued as Steed Malbranque charged down an attempted Senderos clearance only to clip a shot well side.
And the hosts were made to pay in the 33rd minute when Kakuta took advantage of some poor defending. The 19-year-old was picked out by Zamora all alone in the middle of the area and he poked the ball through the legs of Simon Mignolet.
Sunderland should have responded immediately but Lee Cattermole's finish from 10 yards out was weak and easily saved by Schwarzer after a superb ball from makeshift frontman Stephane Sessegnon, while Sulley Muntari saw an effort deflected just over the bar.
Sessegnon had a chance to run at the Fulham defence five minutes into the second half and he engineered a shooting chance but his effort lacked power and Schwarzer safely held on.
Fulham were inches away from grabbing a second moments later as a sliding Zamora just failed to turn Gudjohnsen's cross-shot into an empty net.
The Cottagers did double their advantage in the 61st minute with a goal from Davies that was as simple as it was clinical. Steve Sidwell chased a long ball to the byline and cut it back for Davies to guide his shot into the far corner.
Both managers turned to their substitutes, with Jonathan Greening replacing Kakuta while Steve Bruce took off Muntari and sent on centre-back Anton Ferdinand, with Nedum Onuoha moving up front to offer some much-needed height and power.
It was game over in the 73rd minute as Davies grabbed his second of the afternoon. Mignolet and Ferdinand got in each other's way as they attempted to clear Zamora's cross and Davies turned the loose ball home despite the best efforts of Elmohamady.
That was the cue for large sections of the Sunderland fans to head for the exits and there was no doubt which team was in the ascendancy now.
Gudjohnsen tried his luck from 25 yards with a volley that landed just wide of the post while Sunderland continued to huff and puff without ever threatening to breach Schwarzer's goal.