Martin O'Neill's side, who had scored only seven goals and won just once in 10 league games prior to Sunday, found the net three times in 20 minutes in the second half.
Strikes from Steven Fletcher, Carlos Cuellar and a screamer off the post from Stephane Sessegnon wrapped up the points in the 69th minute against a Fulham side reduced to 10 men.
The balance turned in Sunderland's favour when Fulham's Norway centre-back Brede Hangeland was shown a straight red card by referee Lee Probert after a reckless lunge on Lee Cattermole with an hour still to play.
Sunderland took the lead when Fletcher scored in the 50th minute - 15 seconds after Fulham's John Arne-Riise hit the bar at the other end.
Fulham equalised when substitute Mladen Petric hooked the ball home from close range but after that Sunderland took control.
Although they only climbed one place to 15th, Sunderland moved on to 12 points from 11 games, three clear of Aston Villa who are 18th. Fulham are ninth with 16 points.
Champions Manchester City went top of the table for the first time this season when they beat Aston Villa 5-0 on Saturday while Manchester United lost 1-0 at Norwich City.
