The Toffees started the game looking to leapfrog both Spurs and Bolton into fifth spot while Chris Coleman's stuttering team were only five points ahead of 18th-placed Sheffield United.
A stinging drive from Mikel Arteta on ten minutes forced Antti Niemi to make a decent save and sparked the game into life as the home side signalled their intent.
But Everton's defence were having their own troubles in the early stages and, after a comedy of errors, it was no surprise when Fulham went ahead.
Old boy Simon Davies whipped in a cracking corner for a completely unmarked Carlos Bocanegra to head home in the 22nd minute.
Three minutes later though Lee Carsley got Everton level after good work by Arteta and Joleon Lescott.
The Republic of Ireland international, who had a heavily bandaged head after an early clash with Zat Knight, poked the ball past Niemi with the outside of his right foot from eight yards out after being fed a lovely ball by the outstanding Lescott.
James Vaughan missed a sitter on 30 minutes after Andrew Johnson had forced a fine save from Niemi. The ball cannoned off the keeper's palms but Vaughan failed to get his disappointing shot on target.
A rare Alan Stubbs goal put Everton in front seven minutes later. Arteta put in an inviting free-kick that the veteran defender headed into the pitch before it bounced over a despairing Niemi.
Vaughan almost made it 3-1 when he unluckily hit the woodwork after sprinting onto Lescott's cross. The youngster just got his toe to the ball from three yards out but saw his effort ricochet agonisingly back off the upright.
He made no mistake though on the stroke of half-time when he buried his shot into the Fulham net after latching onto a smart Arteta ball after good work by Johnson near the corner flag.
In the second half Brian McBride almost pulled one back for the Londoners with a glancing header that just went the wrong side of Tim Howard's post.
Fulham huffed and puffed and created a couple of half-chances but Everton were by far the classier side, and when substitute Victor Anichebe made it four, it was just reward for a concerted team effort.