Collins John and Brian McBride scored in the first half to leave Everton with work to do in order to finish the season in fourth spot.
The Cottagers needed a win to take them clear of the bottom three and their double strike means manager Chris Coleman can finally start looking towards next season.
The two sides headed to Craven Cottage fighting battles at either end of the Premiership table but the early stages signalled Everton's intent to keep up their push for Europe.
A direct start led to early danger for the home side and Everton thought they had gone ahead within the first minute.
Kevin Kilbane touched the ball into the net following a flicked header by David Weir. The away supporters celebrated at the opposite end, but their cheers were cut short as it became clear the goal had been ruled out for offside.
The Toffees refused to break the pace of the game and moments later Tim Cahill broke forward. His shot was weak however, and failed to trouble Edwin Van der Sar as it trickled wide.
It proved to be Cahill's last major say in the game, as ten minutes later he limped off after picking up a leg injury and was replaced by Leon Osman.
The substitution seemed to signal a change in dominance as Fulham stepped up a gear and almost immediately got their reward.
On 15 minutes Liam Rosenior crossed from the right and Tomasz Radzinski's snap shot was blocked by Mikel Arteta. The ball fell kindly for John though and the striker took a touch before sweeping the ball into the roof of the net to give Fulham the lead.
The goal silenced Everton's travelling support and the Cottagers continued to heap pressure on the Champions League chasers.
Papa Bouba Diop hit a hopeful effort over the bar and John had another effort blocked. But eventually Everton did create another opening.
Arteta found Marcus Bent with a throughball, but the Toffees striker struck wide of the far post from a tight angle.
Van der Sar was forced into the only real save of the first half on 37 minutes as he got down well to keep out a header from Duncan Ferguson.
And with seven minutes of the first period remaining Fulham doubled their lead in style. Lee Clark released Luis Boa Morte down the left, who teased the Everton defence.
He then delivered a deep cross in to the penalty area which McBride rose to meet and expertly guided a header into the top corner of Nigel Martyn's net.
After the break Everton came out with all guns blazing, and should have given themselves a lifeline within two minutes of the restart.
Ferguson's flick header landed at the feet of Lee Carsley, but with just the Fulham goalkeeper to beat he hit a panicked shot wide of the target.
With 25 minutes left Everton manager David Moyes introduced forwards James Beattie and James McFadden in a desperate attempt to find a way back into the game.
And their hopes were furthered as Diop was sent off for a second bookable offence 15 minutes from time.
The midfielder held back Kilbane and Steve Bennett immediately sent him for an early shower. The Toffees hoped the extra man may give them a way back but it was not to be.
Beattie came close with a free-kick in the final minute, but it was Fulham who held out for a vital three points.
Man of the Match: Lee Clark - The Cottagers skipper led by example with an all-action performance that drove his side on to victory and Premiership survival.