Marouane Fellaini's second-half header sent Everton into the last 16 of the FA Cup as they came from behind to beat Fulham at Goodison Park.
Danny Murphy handed Fulham an early lead when he slotted home from the spot after Johnny Heitinga was punished for a handball in the area.
However, Denis Stracqualursi put Everton level with a deft header from Landon Donovan's cross soon after.
Fellaini grabbed a deserved winner as he headed home another Donovan cross.
Everton had never beaten Fulham in the FA Cup before this game with the Cottagers having won all four of their previous meetings in the competition.
did you know?
Fulham have not won at Goodison Park since an FA Cup victory back in 1975
However, Martin Jol's side have been woeful on the road this season - their only away league victory came back in October at Wigan.
Despite that, it was the visitors who got off to the better start as Everton defender Heitinga was adjudged to have handled in the area.
The Dutchman slid in to block Chris Baird's strike and the ball came off his arm, with referee Howard Webb pointing to the spot without delay.
Murphy stepped up to send Tim Howard the wrong way with his calmly taken penalty and grab his sixth goal of the season.
Everton were incensed by the penalty decision but going behind jolted them into life and they should have equalised soon after when Shane Duffy headed wide from close range after he rose to meet Magaye Gueye's cross.
Tim Cahill, who scored his first goal since 2010 on Saturday against Blackburn, was denied a second of the season when David Stockdale made a superb save to push away his headed attempt.
Stephen Kelly was then the hero when he headed a Duffy shot off the line, but Everton's pressure soon paid off.
Donovan made space down the right-hand side before crossing for Stracqualursi, whose deft header gave Stockdale no chance.
did you know?
This was the eighth time in four seasons that Everton have had to face fellow Premier-League opposition in the FA Cup
Bryan Ruiz had Fulham's best chance before the break to put the Cottagers back in front but he hit a tame effort straight at Howard when there were better options on offer.
Everton pushed forward after the break but Stockdale was alert again to deny Stracqualursi, the Fulham goalkeeper diving at his feet to take the ball.
Andy Johnson was making his first start of 2012 but his first real action came when he hit a tame shot straight at Howard from inside the area just after the hour mark.
The game seemed to be petering out into a draw, but Donovan had other ideas as he turned provider once again.
Phil Neville played him in down the right and he sent in a perfectly placed cross for Fellaini to head back across goal and past Stockdale.
Jol introduced Bobby Zamora in a desperate attempt to earn a replay but even the England international could not change the course of the tie with Ruiz wasting their best chance to grab a dramatic equaliser when he fired a volley wide from inside the area.
Everton assistant manager Steve Round:
"We just about deserved it, we had the better chances.
"The penalty came against the run of play and it was a difficult one for the referee to give. It hit Heitinga's hand but we need some clarification on what is handball, and what isn't. There is a real inconsistency there.
"The team showed great sprit to come back and win it and every time we put the ball in the box we looked a threat.
"I'm really pleased for Denis Stracqualursi, he works so hard and he just needs to get the breaks.
"We're trying very hard to add to the squad before the transfer deadline but there is no real news at the moment."
Fulham manager Martin Jol:
"If you score a goal that early, you hope for more. You hope to go to the next round.
"But you have to defend well because you know the quality they have from crosses and midfield players.
"They had a strong spell of five corners in about two minutes, that is their strength. Under pressure you have to play around them and we couldn't do that most of the time.
"The result is disappointing but overall I think Everton deserved it."
Live Text Commentary
Full Time The final whistle goes and the game is over.90:00 +3:08
Unfair challenge on Phil Neville by Steve Sidwell results in a free kick. Landon Donovan takes the direct free kick.90:00 +1:04
Outswinging corner taken left-footed by Royston Drenthe from the left by-line.90:00 +0:54
Victor Anichebe takes a shot. Blocked by Brede Hangeland.90:00 +0:10
Bryan Ruiz produces a left-footed shot from deep inside the penalty area which goes wide of the right-hand post.88:57
Unfair challenge on Landon Donovan by Bryan Ruiz results in a free kick. Tim Howard takes the direct free kick.88:08
Andrew Johnson fouled by Phil Neville, the ref awards a free kick. Free kick crossed left-footed by Bryan Ruiz, clearance by Darron Gibson.85:56
Johnny Heitinga restarts play with the free kick.85:56 Substitution
Substitution Marcello Trotta comes on in place of Danny Murphy.85:56 Booking
Booking Clint Dempsey shown a yellow card.85:48
Free kick awarded for an unfair challenge on Royston Drenthe by Steve Sidwell.82:38
Direct free kick taken by David Stockdale.82:38 Substitution
Substitution Denis Stracqualursi leaves the field to be replaced by Victor Anichebe.82:38
Unfair challenge on Danny Murphy by Landon Donovan results in a free kick.81:46 Substitution
Substitution Chris Baird leaves the field to be replaced by Steve Sidwell.81:01
Aaron Hughes fouled by Denis Stracqualursi, the ref awards a free kick. Aaron Hughes takes the direct free kick.80:40
Unfair challenge on Danny Murphy by Darron Gibson results in a free kick. Free kick taken by Chris Baird.78:33
Bobby Zamora gives away a free kick for an unfair challenge on Marouane Fellaini. Tim Howard takes the direct free kick.77:55
Free kick taken by Danny Murphy.77:55 Substitution
Substitution Damien Duff goes off and Bobby Zamora comes on.
Brede Hangeland fouled by Denis Stracqualursi, the ref awards a free kick.76:37
Outswinging corner taken right-footed by Landon Donovan, Brede Hangeland makes a clearance.76:18
Tim Cahill takes a shot.72:57
Landon Donovan provided the assist for the goal.72:57 Goal scored
Goal! - Marouane Fellaini - Everton 2 - 1 Fulham Marouane Fellaini grabs a headed goal from deep inside the penalty area. Everton 2-1 Fulham.72:12
Phil Neville delivers the ball from the free kick right-footed from right wing. Landon Donovan delivers the ball,72:12 Booking
Booking Chris Baird is shown a yellow card for unsporting behaviour.72:02
Chris Baird concedes a free kick for a foul on Landon Donovan.69:32
Landon Donovan has an effort at goal from outside the penalty box missing to the wide left of the goal.67:24 Substitution
Substitution Royston Drenthe replaces Magaye Gueye.66:47
Brede Hangeland is adjudged to have handled the ball. Direct free kick taken by Phil Neville.64:16
Foul by Phil Neville on Clint Dempsey, free kick awarded. Damien Duff delivers the ball from the free kick right-footed from left wing, clearance made by Shane Duffy.63:44
Shot by Denis Stracqualursi from a long way out goes over the target.62:04
Andrew Johnson takes a shot. Save made by Tim Howard.60:03
Free kick awarded for an unfair challenge on Phil Neville by Clint Dempsey. Phil Neville takes the free kick.58:57
Inswinging corner taken left-footed by Bryan Ruiz played to the near post, Tim Cahill makes a clearance.57:54
Foul by Stephen Kelly on Magaye Gueye, free kick awarded. Free kick crossed left-footed by Leighton Baines.57:13
Clint Dempsey takes a shot. Blocked by Shane Duffy.56:09
Danny Murphy restarts play with the free kick.56:09 Booking
Booking The referee books Tim Cahill for unsporting behaviour.55:41
Tim Cahill gives away a free kick for an unfair challenge on Andrew Johnson.55:01
Foul by Aaron Hughes on Tim Cahill, free kick awarded. Landon Donovan takes the direct free kick.51:21
Header from deep inside the area by Clint Dempsey goes over the bar.49:58
Andrew Johnson is ruled offside. Free kick taken by Tim Howard.49:26
Bryan Ruiz takes a shot. Johnny Heitinga gets a block in.45:01
The second half has started.45:00 +1:57 Half time
Half Time The match has reached half-time.44:24
Landon Donovan takes a shot. Tim Cahill gets a block in. Tim Cahill has an effort at goal from just inside the box that misses to the right of the target.40:38
Landon Donovan takes a shot. Save made by David Stockdale.39:18
Danny Murphy fouled by Tim Cahill, the ref awards a free kick. Danny Murphy takes the direct free kick.36:43
Chris Baird takes a shot. Bryan Ruiz gets a block in. Bryan Ruiz takes a shot. Save by Tim Howard.36:08
Free kick taken by Danny Murphy.36:08 Booking
Booking Darron Gibson is cautioned.36:03
Foul by Darron Gibson on Andrew Johnson, free kick awarded.35:01
Andrew Johnson concedes a free kick for a foul on Leighton Baines. Direct free kick taken by Tim Howard.31:22
Free kick awarded for an unfair challenge on Johnny Heitinga by Andrew Johnson. Tim Howard takes the direct free kick.30:18
Inswinging corner taken left-footed by Damien Duff from the right by-line.28:51
Marouane Fellaini has an effort at goal from outside the box which misses left.26:43
Assist by Landon Donovan.26:43 Goal scored
Goal! - Denis Stracqualursi - Everton 1 - 1 Fulham Denis Stracqualursi finds the net with a headed goal from inside the box. Everton 1-1 Fulham.23:33
Unfair challenge on Andrew Johnson by Shane Duffy results in a free kick. Danny Murphy restarts play with the free kick.22:36
Landon Donovan takes a inswinging corner.22:23
Shane Duffy takes a shot. Stephen Kelly manages to make a clearance.22:01
Corner taken by Landon Donovan from the left by-line.21:40
Magaye Gueye takes a inswinging corner to the near post, clearance by Chris Baird.21:14
Landon Donovan takes the inswinging corner, Tim Cahill takes a shot. Save by David Stockdale.20:27
Corner taken right-footed by Landon Donovan, Magaye Gueye takes a shot. Aaron Hughes gets a block in.19:59
Inswinging corner taken by Magaye Gueye, save by David Stockdale.19:23
Foul by Chris Baird on Landon Donovan, free kick awarded. Phil Neville takes the direct free kick.16:54
Tim Cahill fouled by Danny Murphy, the ref awards a free kick. Direct free kick taken by Phil Neville.15:54
Corner taken by Magaye Gueye, Headed effort from close range by Shane Duffy goes wide left of the target.15:20
Denis Stracqualursi fouled by Stephen Kelly, the ref awards a free kick. The free kick is swung in left-footed by Leighton Baines, John Arne Riise manages to make a clearance.12:35 Booking
Booking Johnny Heitinga goes into the referee's book.13:03 Goal scored
Goal! - Danny Murphy - Everton 0 - 1 Fulham Danny Murphy scores a placed penalty. Everton 0-1 Fulham.12:32
Johnny Heitinga is penalised for handball and concedes a .12:08
Damien Duff takes a shot. Johnny Heitinga gets a block in.5:35
Unfair challenge on Phil Neville by Clint Dempsey results in a free kick. Phil Neville takes the free kick.2:30
Darron Gibson concedes a free kick for a foul on Bryan Ruiz. Free kick taken by Danny Murphy.1:24
Long range shot by Clint Dempsey goes wide right of the target.0:41
Phil Neville gives away a free kick for an unfair challenge on John Arne Riise. John Arne Riise takes the free kick.0:00
The game kicks-off.
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