Brian McBride's second-half header gave Fulham a ray of hope in their battle to avoid Premier League relegation but dented Everton's European dreams.
Joseph Yobo flicked Simon Davies' cross into McBride's path and the American headed past the helpless Tim Howard.
Everton's best chance came through Yakubu who forced Kasey Keller into a fine save, but they created little.
Davies should have doubled Fulham's lead but he failed to convert Jimmy Bullard's delightful pass.
Interview: Fulham manager Roy Hodgeson This was only Fulham's fourth victory in the Premier League and leaves the Londoners effectively four points from safety because of their inferior goal difference.
Roy Hodgson's men deserved the win and the smiles on his players' faces when the final whistle blew illustrated how crucial a victory this could prove to be.
Fulham have matches against fellow strugglers Newcastle, Derby, Sunderland, Reading and Birmingham remaining and survival could be within their grasp.
The red half of Merseyside will also be happy as Everton are still three points behind fourth-placed Liverpool in the chase for the final Champions League spot, having now played the same number of games.
Fulham started brightly, with Bullard, Danny Murphy and Davies prominent in midfield.
Indeed, it was former Everton player Davies who created Fulham's best chance of a poor first half with his cross creating space for McBride, whose toe-poked volley whistled past Howard's left-hand post.
When Andrew Johnson limped off injured after 15 minutes Fulham sensed that this could be their day.
Right-back Tony Hibbert replaced the England international, as Everton did not have a striker on the substitutes' bench, and consequently the visitors posed little threat in attack.
Facing the strong wind, David Moyes' men struggled and only in the final minutes of the first half did they force Keller into action. Yakubu was allowed time and space to turn inside the box and his shot forced the Fulham goalkeeper to dive low to his left.
Both teams started the second half with greater attacking intent.
Eddie Johnson's pace posed the Merseysiders problems and his jinking run on the hour forced the visitors to concede a corner, from which the American should have done better, but the striker's header was way off target.
Johnson's miss would not prove costly, however, as Davies and McBride combined for a deserved goal, the striker's second of an injury-plagued season.
Yobo unintentionally flicked Davies's cross into McBride's path and the American's downward header into the corner gave compatriot Howard no chance.
The defender had a chance to make amends minutes later but he wastefully headed wide when unchallenged in the box.
In the closing stages, Davies - standing inside the box - had a great opportunity to put the game to bed but the midfielder failed to do justice to the industrious Bullard's magnificent pass.
When referee Steve Bennett brought the game to an end however Fulham did not give one jot about their profligacy as McBride's solitary strike was enough to give them the points that they so desperately needed.
"We can look forward to the last eight games with optimism. We started extremely brightly but Everton know how to defend and grind out results.
"The goal was vital. For us the difference between one and three points in the match was everything."
We did not play well at all. We have never been very good at Craven Cottage and this was the same.
The players are a good group who have done well. We would have settled for where we are if we had been offered this at the start of the season."
Interview: David Beckham 
