Nikica Jelavic scored twice as Everton moved a step closer to their goal of finishing above Liverpool with an emphatic victory at Goodison Park.
The Croatian struck twice before half-time, with Marouane Fellaini adding another to make it 3-0 at the interval.
Substitute Tim Cahill added a fourth on the hour mark, as Fulham fell apart.
The victory moves Everton into seventh place in the Premier League table, two points clear of their great Merseyside rivals with three games remaining.
The Toffees are finishing the season as strongly as anyone, with manager David Moyes determined to secure the eighth top-eight finish of his 11-year tenure.
Everton have not finished above Liverpool in the Premier League table since 2005 but they have now scored four goals in three consecutive league games.
Much of that has been down to the form of Jelavic, who signed from Rangers in January. And he stole the show again, this time at the expense of Fulham's defenders.
Cottagers manager Martin Jol missed the trip to Merseyside with a chest infection, leaving first-team coach Billy McKinlay in charge for the day.
If that illness had not been enough to rule Jol out, a quick glance at the record books might have left the Dutchman feeling sick.
Fulham had lost their previous 18 matches at Goodison Park, their last victory coming in February 1948, their last point in 1959.
David Moyes Everton manager
“We have played as well as any team in the Premier League since January”
Recent history also provided Everton supporters with confidence. The same side that held Manchester United to a 4-4 draw at Old Trafford took the field and began where they left off last Sunday.
Sharper to the ball, swifter to use it, Everton snatched the initiative from the off.
Steven Pienaar's quick feet won an early free-kick as Moussa Dembele lunged in. Jelavic's curling effort only got as far as Pavel Pogrebnyak, who raised his hand in front of his face to block the ball while standing in the penalty area.
Referee Phil Dowd had no hesitation in pointing to the spot. Jelavic made no mistake, taking his tally to nine goals since his move to Merseyside.
The Croatian striker almost scored a second minutes later, latching onto Phil Jagielka's long ball, outmuscling Brede Hangeland only to fire his shot against the right-hand upright. A minute later Fellaini did double the lead, heading in unmarked from a right-wing corner.
Fulham had chances and might have pulled a goal back but for a fantastic save by Tim Howard.
Clint Dempsey's deflected shot appeared to have wrong-footed the American goalkeeper, but he quickly changed direction, thrusting his right hand up to deflect the shot up and over the bar.
Everton were in command, though. A delightfully weighted pass by Pienaar sent Jelavic clear, he beat a charging Mark Schwarzer to the ball, turned and shot beyond the lone Fulham defender on the line.
The second half offered little respite for the visitors. Cahill, who replaced the injured Darron Gibson at half-time, added a fourth on the hour mark, latching onto Pienaar's chipped through-ball to beat Schwarzer.
Jelavic came within a whisker of his hat-trick with a curling free-kick, but Schwarzer came to Fulham's rescue on a day they will want to forget.
Everton manager David Moyes: "The two early goals helped us control the game. It was a really good performance and three important points. I enjoyed the way we played, we played some really good football.
"I think we have played as well as any team in the Premier League since January. It is what we have done over recent years. Some teams start the season at the top of the league and fade away. We start at the bottom and rise up and get better near the end of the season.
"We feel if we can get the ball anywhere near Nikica Jelavic in the box, we have a chance. To score another two today, albeit one a penalty, was a fantastic return."
Fulham first-team coach Billy McKinlay:
"We never turned up. That wasn't us today. There are a lot of disappointed guys in the dressing room. The manner of the defeat was disappointing.
"We have come here confident we could get a result but credit to Everton they put us under a lot of pressure. Losing an early goal doesn't help you, but I don't think we got started all game. I have had a look at the penalty and if it was in our box we would have been looking for penalty kick, we have no complaints.
"Hopefully Martin [Jol] should be back on on Tuesday, he has a chest infection and was advised just to rest up for a couple of days. Hopefully we will see him on Tuesday."
Live Text Commentary
Full Time The match has reached full-time.89:20
Unfair challenge on Clint Dempsey by Tim Cahill results in a free kick. Danny Murphy takes the free kick.87:47
Kerim Frei is caught offside. Phil Jagielka takes the indirect free kick.86:16
Tim Cahill gives away a free kick for an unfair challenge on Moussa Dembele. Danny Murphy restarts play with the free kick.85:14
The referee blows for offside against Sylvain Distin. Chris Baird restarts play with the free kick.83:35
Aaron Hughes fouled by Nikica Jelavic, the ref awards a free kick. Free kick taken by Aaron Hughes.82:52
Direct free kick taken by Johnny Heitinga.82:52 Substitution
Substitution Magaye Gueye joins the action as a substitute, replacing Steven Pienaar.82:52
Dickson Etuhu gives away a free kick for an unfair challenge on Ross Barkley.82:26
Tim Cahill challenges Moussa Dembele unfairly and gives away a free kick. Free kick taken by Moussa Dembele.81:47 Substitution
Substitution (Fulham) makes a substitution, with Dickson Etuhu coming on for Mahamadou Diarra.80:59
Leon Osman takes a shot. Save by Mark Schwarzer. Outswinging corner taken from the right by-line by Ross Barkley.80:43
Short corner taken by Ross Barkley.80:27
Steven Pienaar takes a shot. Mark Schwarzer makes a save.78:35
Tim Cahill takes the direct free kick.78:35 Booking
Booking Mahamadou Diarra booked for unsporting behaviour.78:21
Free kick awarded for a foul by Mahamadou Diarra on Ross Barkley.74:39 Substitution
Substitution Marouane Fellaini leaves the field to be replaced by Ross Barkley.73:08
Nikica Jelavic is ruled offside. Mark Schwarzer takes the free kick.72:12
Phil Neville takes a shot. Blocked by Brede Hangeland.
Foul by Chris Baird on Nikica Jelavic, free kick awarded. Johnny Heitinga takes the direct free kick.68:51
Unfair challenge on Danny Murphy by Tim Cahill results in a free kick. Danny Murphy takes the free kick.65:26 Substitution
Substitution Danny Murphy replaces Pavel Pogrebnyak.63:52
Moussa Dembele challenges Nikica Jelavic unfairly and gives away a free kick. Nikica Jelavic produces a strike on goal direct from the free kick, save by Mark Schwarzer.63:40
Clint Dempsey takes a shot. Johnny Heitinga gets a block in.63:06
Leon Osman challenges Kerim Frei unfairly and gives away a free kick. Kerim Frei restarts play with the free kick.61:20
Aaron Hughes fouled by Nikica Jelavic, the ref awards a free kick. Mark Schwarzer takes the direct free kick.59:38
Assist on the goal came from Steven Pienaar.59:38 Goal scored
Goal! - Tim Cahill - Everton 4 - 0 Fulham Goal scored by Tim Cahill from deep inside the penalty box to the bottom right corner of the goal. Everton 4-0 Fulham.57:20
The assistant referee flags for offside against Chris Baird. Free kick taken by Tim Howard.55:24
Tim Cahill challenges Mahamadou Diarra unfairly and gives away a free kick. Free kick taken by John Arne Riise.51:45
Free kick awarded for a foul by Phil Neville on Moussa Dembele. Free kick taken by John Arne Riise.45:01
The second half has started.45:01 Substitution
Substitution Chris Baird on for Philippe Senderos.45:01 Substitution
Substitution Tim Cahill is brought on as a substitute for Darron Gibson.45:00 +2:08 Half time
Half Time The referee calls an end to the first half.45:00 +0:55
Clint Dempsey takes a shot. Phil Jagielka gets a block in. Damien Duff takes a inswinging corner from the right by-line to the near post, Nikica Jelavic makes a clearance.44:54
Mahamadou Diarra gives away a free kick for an unfair challenge on Leon Osman. Darron Gibson restarts play with the free kick.43:46
Corner taken left-footed by Damien Duff, Phil Jagielka manages to make a clearance.42:48
Direct free kick taken by Mahamadou Diarra.42:48 Booking
Booking Darron Gibson goes into the referee's book for unsporting behaviour.42:42
Free kick awarded for an unfair challenge on Clint Dempsey by Darron Gibson.39:05
Assist by Steven Pienaar.39:05 Goal scored
Goal! - Nikica Jelavic - Everton 3 - 0 Fulham A goal is scored by Nikica Jelavic from deep inside the penalty box to the bottom left corner of the goal. Everton 3-0 Fulham.31:37
Leon Osman fouled by Mahamadou Diarra, the ref awards a free kick. Direct free kick taken by Darron Gibson.30:26
Clint Dempsey takes a shot. Blocked by Johnny Heitinga. Corner taken by Damien Duff from the right by-line, Nikica Jelavic manages to make a clearance.29:17
The referee penalises Nikica Jelavic for handball. Brede Hangeland takes the direct free kick.28:52
Clint Dempsey produces a right-footed shot from just outside the area that goes harmlessly over the bar.25:01
Pavel Pogrebnyak takes a shot. Johnny Heitinga gets a block in.24:34
Free kick awarded for a foul by Johnny Heitinga on Pavel Pogrebnyak. Mahamadou Diarra takes the free kick.22:23
Inswinging corner taken by Damien Duff, save made by Tim Howard.21:11
Nikica Jelavic is flagged offside by the assistant referee. Philippe Senderos takes the free kick.18:17
Aaron Hughes fouled by Phil Neville, the ref awards a free kick. Mark Schwarzer takes the free kick.15:43
Assist on the goal came from Steven Pienaar.15:43 Goal scored
Goal! - Marouane Fellaini - Everton 2 - 0 Fulham Marouane Fellaini scores a headed goal from deep inside the penalty box. Everton 2-0 Fulham.15:04
Outswinging corner taken from the right by-line by Steven Pienaar,14:30
Shot by Nikica Jelavic from inside the penalty area hits the post.11:19
Philippe Senderos concedes a free kick for a foul on Marouane Fellaini. Johnny Heitinga has a direct shot on goal from the free kick.10:14
Kerim Frei takes a shot. Tim Howard makes a save. Corner taken left-footed by Damien Duff from the right by-line, Nikica Jelavic makes a clearance.7:37
Marouane Fellaini challenges Mahamadou Diarra unfairly and gives away a free kick. Mahamadou Diarra restarts play with the free kick.6:26 Goal scored
Goal! - Nikica Jelavic - Everton 1 - 0 Fulham Power penalty scored by Nikica Jelavic. Everton 1-0 Fulham.4:05
Moussa Dembele concedes a free kick for a foul on Steven Pienaar. Nikica Jelavic fires a strike on goal direct from the free kick, Nikica Jelavic gets a block in. Handball by Pavel Pogrebnyak.3:10
Marouane Fellaini takes a shot. Blocked by Brede Hangeland.2:05
The referee blows for offside. Indirect free kick taken by Mark Schwarzer.0:00
The match gets underway.
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