A double from Nikica Jelavic and an outstanding display from the on-loan Steven Pienaar helped Howard's in-form Toffees sweep aside Dempsey and the dismal Cottagers.
U.S. international Tim Howard recorded the shutout while keeping fellow American at 16 league goals.
On the back of their 4-4 draw at Old Trafford with title-chasing Manchester United, Everton manager David Moyes named an unchanged side, meaning Fellaini continued in his attacking midfield role behind lone striker Jelavic.
Fulham, without a win at Goodison Park in 40 top-flight visits and without Martin Jol on the touchline due to illness, called exciting Swiss winger Kerim Frei into their starting lineup, club captain Danny Murphy dropping to the bench.
Nikica Jelavic has made quite an impact at Goodison Park since his January arrival from Rangers and Everton's took a mere six minutes to score his eighth goal in his last seven appearances for the Toffees.
The Croatian striker saw his 25-yard free kick blocked by the arm of Pavel Pogrebnyak in the Fulham wall and referee Phil Dowd showed no hesitation in pointing to the penalty spot, and Jelavic coolly converted from 12 yards.
In the opening 10 minutes Fulham barely made its way past the halfway line, but it signalled its intent to get back into the match in the 11th, with clever work from Moussa Dembele teeing up a chance for the fleet-footed Frei. But after evading the challenge of Tony Hibbert, his drive was comfortably turned behind by Howard.
However, the Toffees were on the back foot soon after when a long ball from Heitinga put Jelavic clean through on goal but from the angle he hit the outside of Mark Schwarzer's post.
The Fulham defense continued to be at sixes and sevens and looked susceptible to the forward runs, cutting in from the right of Leon Osman, and his good work indirectly led to Everton's second goal.
After more clever play from Jelavic, Osman's shot was blocked behind by Hangeland but from the resulting corner, a free header from the unmarked Fellaini beat Schwarzer and doubled the home sides lead.
Clearly buoyed by the confidence of its recent good form and its bright start, Everton continued to play with a wonderful style and panache, the likes of Osman and Pienaar exchanging quick passes and interchanging positions.
Fulham has had one of the Premier League's outstanding performers this season in Dempsey, but his United States teammate Howard isn't short of quality either, as the Everton 'keeper proved in the 31st minute, to deny the away side a foothold in the match.
Aaron Hughes' cross from the right was nodded down by Pogrebnyak into the path of Dempsey, and just when he may have thought that his rising strike from 15 yards was set to make the net bulge, he was denied by a brilliant save from Howard.
If that save denied Fulham a lifeline, then Jelavic's second in the 39th minute ended the contest.
Steven Pienaar strode through midfield before feeding a pass beyond the Fulham backline for Jelavic to run onto and while a combination of his heavy touch and the advancing Schwarzer initially sent him wide, he went unchallenged and was allowed to turn back inside before drilling a low shot through the keeper's legs and into the back of the net, for nine goals in seven games and 10 since his arrival in English football.
At halftime Moyes made one change to his lineup, replacing Darron Gibson, who picked up a booking late in the first half, with Tim Cahill. The move saw Fellaini drop into a holding midfield role and Cahill move into an advanced position supporting Jelavic.
With the game all but won, Everton started the second half at a leisurely pace but in the 60th minute felt the need to re-assert its dominance with a fourth goal and once again it owed much to the stealthy running of Pienaar.
A lengthy spell of passing had some pace injected into it by the South African playmaker, who played a clever one-two to evade the Fulham midfield, before scooping a wonderful through pass to the on-rushing Cahill who stretched and diverted the ball past the helpless Schwarzer.
Five minutes later, Jelavic almost completed his hat trick, curling a 25-yard free kick over the wall, only to be denied by Schwarzer at full stretch.
Everton continued to look comfortable against a Fulham side which looked to have given up the ghost, all apart from their Australian keeper Schwarzer who denied Osman with two smart saves in the space of a minute late in the game.
With seven minutes remaining Goodison rose to acclaim the performance of Pienaar, as he was replaced by Royston Drenthe, the on-loan Tottenham midfielder having been at his effervescent best, and who, teamed with Jelavic, has given Moyes side quite the cutting edge.