They started the game on the back of four successive home wins and boss David Moyes only made one change to the line-up that drew with West Ham United last week, replacing Sander Westerveld in goal with Richard Wright.
Chris Coleman included former Everton player Mark Pembridge in his side as well as American Carlos Bocanegra following their 4-0 home defeat to Arsenal last weekend.
In the first minute Spanish midfielder Mikel Arteta cut into the box, but he over-hit his cross.
The home side closed down possession well and were camped in the opposition half. A free-kick just outside the box was Fulham's first attempt on goal in the tenth minute but it was easily cleared. Luis Boa Morte was next to probe, but his free-kick again was cleared.
Disaster struck for the away side in the 15th minute when James Beattie latched onto a Nuno Valente long ball but he was knocked down by defender Zat Knight.
Uriah Rennie pointed straight to the spot and Beattie slotted the ball into the top left corner past goalkeeper Tony Warner.
Fulham's first effort on target was Zat Knight's header from Simon Elliott's free-kick in the 22nd minute, but it was comfortably saved by keeper Wright.
Everton probed down both flanks and Beattie could have made it 2-0 from Valente's cross in the 30th minute but he headed wide.
The home team's moves were crisp, mainly through the bright Arteta, but the finishing touch was lacking.
Alan Stubbs had a clear header from a corner but directed it over the bar.
In the 35th minute Arteta was sent clear through after a neat one-two with Jamie McFadden but then shot straight at the goalkeeper.
A minute later Beattie scored his and Everton's second goal. Tim Cahill laid off a long free-kick from Stubbs to Beattie. His curling shot from the edge of the box looped over Warner into the top corner.
Fulham pushed forward as the half came to a close but did not threaten Richard Wright's goal.
Arteta had the first chance of the second half but he volleyed tamely from Leon Osman's cross. Two minutes later he returned the favour to Osman, but the small midfielder's shot was wide.
Everton then began to get a stranglehold on the game - snuffing out any opposition threat.
A series of dangerous crosses were cleared by Fulham, but this was merely the build-up to the killer blow. In the 58th minute the ball was fired back into the box by David Weir, and Beattie's knock-down set up the oncoming McFadden who volleyed sweetly into the top left corner.
Two minutes later Fulham's frustration boiled over and Steed Malbranque was lucky to escape a yellow card after a late challenge on Phil Neville.
McFadden then had a mazy run in the 63rd minute before being fouled but his free-kick flew narrowly wide.
The Toffees were rampant and Tony Hibbert's cross-cum-shot on 64 minutes beat everybody including keeper Warner, but whistled just wide.
Beattie could have had his third after Arteta released him but he over-hit his volley. Fulham had a half-chance on 71 minutes but Philippe Christanval could not control his shot.
The home side turned the screw with Valente and Hibbert pushing forward.
With five minutes to go Fulham substitute Collins John earned a penalty completely against the run of play after being fouled by Hibbert. He duly converted the spot-kick and almost created a second for Fulham but Brian McBride could not turn in his low cross.
Moyes brought on Dutch midfielder Andy van der Meyde near the end after a long spell out with injury, to a rapturous reception from the Goodison crowd.
McBride nearly caused some more Everton jitters but Wright made a good save from close range from his scrambled effort.