Martin O'Neill's men secured their first win in six games at Craven Cottage, with Martin Jol's side losing captain Brede Hangeland to a red card after just half an hour
Mladen Petric temporarily pulled the visitors level after Steven Fletcher's second-half opener, but goals from Carlos Cuellar and Stephane Sessegnon in quick succession earned the Black Cats a first win in six, with the hosts never recovering from Brede Hangeland's sending off after 30 minutes.
Dimitar Berbatov and Bryan Ruiz continued in attack for the west Londoners, with Damien Duff returning to the side. Martin Jol also handed a full debut to Giorgos Karagounis, who started in Chris Baird's absence through suspension.
The Black Cats were buoyed by Fletcher's inclusion, who overcame fitness concerns to feature at Craven Cottage, while Phil Bardsley and Lee Cattermole were also included after missing out on last week's 2-1 defeat to Everton.
After a dire opening half an hour, in which Steve Sidwell's scuffed effort was the only shot registered on target, a loose pass from Karagounis - symptomatic of the lack of quality in the game - cost Fulham.
The Greek midfielder sold Hangeland short, and after the centre-back lunged to beat the oncoming Cattermole to the ball, referee Lee Probert brandished a red card for what he deemed to be a two-footed tackle, although television replays suggested the decision may have been a little harsh.
Sunderland almost made their advantage count immediately, but Sessegnon was unable to make the most of a free run on goal when played in by Bardsley. Instead of shooting, the ex-PSG man opted to find the run of Fletcher and Aaron Hughes easily cut out the danger.
Berbatov, the focus of much pre-match hype, failed to truly test Simon Mignolet in the opposition goal, with his opportunities limited due to a number of offsides. The Bulgarian soon found space on the right-hand flank as the opening 45 drew to a close, however, but he dragged his shot wide.
John Arne Riise's deflected effort crashed off the bar as the second half began with a flurry of chances resulting in Sunderland taking the lead. Fletcher peeled off substitute Philippe Senderos well to control Adam Johnson's superb ball before calmly poking home beyond Mark Schwarzer.
The hosts were forced into their third change of the evening after the hour mark, with Petric coming on in place of the injured Ruiz, and the striker made an immediate impact. Duff just beat the offside trap before driving the ball across the face of goal for the Croatian to finish.
Yet with Fulham temporarily down to nine men as Petric received treatment off the field, the Black Cats restored their lead and then some. Carlos Cuellar rose to head home his first goal for Martin O'Neill's side, before Sessegnon crashed the ball in off the post with a fabulous strike from 25 yards.
A neat turn set Petric free but the 31-year-old was unable to add to his tally, as Sunderland held on to seal a vital away victory that sees them climb three points clear of the relegation zone.