Liverpool came to life after the break to score four second-half goals.
Garcia scored with a superb header
The visitors probably had the best first-half chance when Brian McBride's shot was well saved by Jose Reina.
But on 52 minutes Dirk Kuyt's shot was handled by Ian Pearce and although Jan Lastuvka saved Steven Gerrard's penalty the Reds captain netted the rebound.
Seven minutes later Jamie Carragher popped up to score, with Luis Garcia's header making it 3-0, before Mark Gonzalez's free-kick completed the win.
Fulham have never won at Anfield but until Gerrard scored with that penalty the visitors hinted they might just come away with a draw.
It is arguable that the loss through injury of Papa Bouba Diop just before the penalty swung the game in Liverpool's favour.
The loss of Diop gave Liverpool the edge in midfield and the home side ruthlessly exploited that advantage.
Diop had been integral to a first-half rearguard action that had stymied Liverpool.
Fulham's determination was also typified by Luis Boa Morte, who curbed his attacking instincts to help out his side's defence on a number of occasions.
The visitors played so well defensively that Lastuvka did not have to make a save until just before half-time when he pushed away Xabi Alonso's shot.
Even so, with Liverpool dominating possession, Lastuvka still had some anxious moments.
Liam Rosenior had to scramble clear Garcia's flick, with the Spaniard also going close with a couple of headers, a portent of what was to come later with that impressive headed goal.
Kuyt probably had Liverpool's best first-half chance when he was picked out by Jermaine Pennant, but the Dutchman miscued with his shot.
Kuyt also claimed a first-half penalty when the ball appeared to hit Pearce's hand, though on that occasion play was waved on.
Fulham might not have had as much possession as Liverpool but they came very close to taking the lead when Reina had to react quickly to push away a McBride effort.
The floodgates opened for Liverpool when Pearce raised his arms to block another Kuyt shot and this time referee Uriah Rennie pointed to the spot.
Lastuvka saved Gerrard's penalty but the ball rebounded to the Liverpool captain, who smashed his shot into the roof of the net.
With the cushion of that lead, some of the anxiety went out of Liverpool's play and they quickly added two more goals.
Defender Daniel Agger played a part in both goals, first flicking the ball to the unmarked Carragher to score his first league goal since Janaury 1999 and then picking out Garcia with a cross from the left.
Lastuvka made a superb reaction save to stop a Gerrard volley, but he could do nothing about Gonzalez's stoppage time free-kick.
Liverpool manager Rafael Benitez:
"After the goal, it was easier. couldn't see it clearly but for me it was a penalty.
"A penalty is a situation which can change a game but we created enough to win, not just with the penalty.
"We had opportunities to score more goals. I think the team was creating enough and we deserved to win."
Fulham manager Chris Coleman:
"I thought we were okay in the first 45 minutes.
"The defining moment was the first goal going in and after that for 15 minutes we fell away. "Our concentration was poor, we lacked a bit of discipline and belief we could get back into it.
"That is something for us to go away and think about."
Liverpool: Reina, Finnan, Carragher, Agger, Riise, Pennant, Alonso, Gerrard, Luis Garcia (Fowler 80), Bellamy (Crouch 77), Kuyt (Gonzalez 72).
Subs Not Used: Dudek, Hyypia.
Goals: Gerrard 54, Carragher 61, Luis Garcia 66, Gonzalez 90.
Fulham: Lastuvka, Volz, Knight, Pearce (Helguson 90), Rosenior, Radzinski, Brown, Diop (Christanval 49), Claus Jensen, Boa Morte, McBride (John 72).
Subs Not Used: Batista, Routledge.
Ref: U Rennie (S Yorkshire).