Liverpool stepped up a gear in the second half to move to within four points of fourth-placed Everton.
The Reds started the game brightly and Luis Garcia fed Fernando Morientes to superbly head in the opening goal.
But Andy Cole levelled with a diving header from Luis Boa Morte's inviting cross and Tomasz Radzinski went close.
The home side dominated proceedings after the break and Sami Hyypia touched in Steven Gerrard's free-kick before Milan Baros netted from close range.
Captain Gerrard had spoken confidently before the game of overhauling their rivals from across Stanley Park in the chase for a Champions League place.
And his team were in front inside 10 minutes when Morientes rose magnificently to head in Garcia's cross from the right.
Fulham, looking to protect an unbeaten Premiership run of five games, were having problems dealing with Liverpool's movement and passing, with Gerrard pulling the strings and Baros, Garcia and Morientes looking lively.
But Lee Clark pounced on a mistake by Garcia to find Boa Mortes, whose centre was met by a high-quality header from Cole and the game was transformed.
Radzinski found space to head Mark Pembridge's corner wide from six yards as Liverpool lost their early fluency.
Much of the unease stemmed from their defensive uncertainty, with the fans sensing their vulnerability on the counter-attack.
The Cottagers, looking for their first win at Anfield, were well marshalled at the back by Zat Knight, although Igor Biscan forced Edwin van der Sar to save low down to his left in the last meaningful action of the first half.
Liverpool pressed straight after the break and van der Sar cleared with his legs from Baros' cross, while Knight had to make a vital interception to deny the Czech striker after John Arne Riise had headed back Jamie Carragher's cross.
Gerrard was then inches over with an acrobatic volley as Fulham struggled to get out of their own half.
It was no surprise when the Reds' pressure paid off with a second goal, as Hyypia got a feint touch to Gerrard's free-kick.
Having relinquished control of the game in the first half after going ahead, Liverpool were in no mood to repeat the mistake.
Baros settled the outcome when he powered home the third from close in after Riise centred from the left.
Gerrard suffered a cut to his head in the build up, although the Anfield faithful were relieved when he re-emerged shortly after.
Boa Morte almost pulled one back in the closing stages, but Djimi Traore produced a timely block following Carlos Bocanegra's cross and Liverpool saw out the game comfortably.
Liverpool boss Rafael Benitez:
"We played well in the first half but after we conceded the goal we started getting nervous.
"The second half we started playing well and after the second goal we had more control. It's three wins in a row which is important for the confidence.
"We have a possibility of reducing the gap between us and Everton for sure. We have 12 more games."
Fulham boss Chris Coleman:
"We worked incredibly hard, and our commitment was superb, but the three goals were poor ones to give away.
"Before their second they weren't threatening much but we lost our concentration and were punished.
"The defending for the third goal was poor all round and we have struggled all season with that. Poor marking in the box has cost us the game."
Liverpool: Dudek, Finnan, Carragher, Hyypia, Traore, Luis Garcia, Gerrard, Biscan (Hamann 65), Riise (Warnock 89), Morientes, Baros (Smicer 82).
Subs Not Used: Pellegrino, Carson.
Booked: Luis Garcia.
Goals: Morientes 9, Hyypia 63, Baros 77.
Fulham: Van der Sar, Rosenior, Knight, Rehman, Bocanegra, Clark, Diop, Pembridge, Radzinski, Cole, Boa Morte.
Subs Not Used: Crossley, Legwinski, McBride, Jensen, Goma.
Booked: Rehman, Diop, Pembridge, Van der Sar.
Goals: Cole 16.
Ref: R Styles (Hampshire).