Danny Collins scored his first goal in nearly two years and only his second for Sunderland as they recorded a third successive win.
The centre-back put Sunderland ahead with virtually the last kick (or head) of the first half to set them on their way to a vital victory.
With Bolton losing, the win put Roy Keane's side 10 points clear of the relegation zone with 15 to play for. On the day of the Grand National, the Black Cats are timing their run to perfection.
Collins' goal gave Sunderland a huge boost after an ordinary performance in the opening period.
Collins thought he had scored in the 15th minute when he headed in Andy Reid's free-kick but referee Mark Halsey scratched it off for pushing. There did not seem to be too much wrong with it.
Just minutes earlier, Brain McBride got free to head Jimmy Bullard's cross straight at Craig Gordon.
Gordon made an even better save just after the break, stopping Kamara's close-range effort.
Keane decided to introduce Michael Chopra after half-time and it was an inspired substitution. Chopra came on for Carlos Edwards and within 10 minutes the striker, playing in midfield, had given Sunderland at 2-0 lead.
Chopra latched on to Kenwyne Jones' flick-on after a long kick by Gordon and lobbed a shot over Kasey Keller, it was another good finish by the former Cardiff man and his 50th career goal.
Sunderland looked to be cruising when Fulham, who are now in deep trouble, pulled a goal back and there was not much Gordon could do about it. David Healy, prolific at international level, curled a peach of a shot into the top corner with his left foot.
It handed the Cottagers brief hope but the Black Cats restored their two-goal cushion with three minutes - and Jones claimed it, his seventh goal of the season.
Dean Whitehead, who put in a real captain's performance, powered into the box and squared it for Jones. The striker's first touch was not great as the ball spun into the air, but he hit a precision right-foot shot into the corner to ease any nerves.
Sunderland's fans were in full voice by this stage - after all, it was the first time they had watched their side win a Premier League game in London for seven years.
After two successive wins away from home and a short trip to Newcastle imminent, "Bring on the Magpies," was the chant from the away end.