Liverpool midfielder Steven Gerrard (C) celebrates scoring their third goal during the English Premier League football match between Fulham and Liverpool at Craven Cottage in London. (AFP/GLYN KIRK)
With seconds of normal time remaining, Reds captain Gerrard stepped up to score from the penalty spot after Sascha Riether fouled Daniel Sturridge.
Gerrard's winner capped an impressive fightback from the visitors, who trailed 1-0 and 2-1, while also cementing Liverpool's hold on fourth place and lifting them to within four points of leaders Chelsea.
Brendan Rodgers' men were twice forced to come from behind on a bizarre evening at Craven Cottage.
A comical own goal by Kolo Toure and another defensive error from central defensive partner Martin Skrtel allowed Kieran Richardson to grab Fulham's second goal.
But Sturridge netted for his seventh league game in a row - the first Anfield star to do so since the Premier League began - before Philippe Coutinho drew them level with 18 minutes remaining to set the stage for Gerrard's winner.
It had been a tougher than expected test for Liverpool, who struggled to get out of the blocks just days after demolishing Arsenal.
Within the opening 60 seconds, Fulham's Ryan Tunnicliffe stung the palms of Simon Mignolet with a shot from the right hand side of the penalty area.
That all came after former Liverpool left-back John Arne Riise launched a long ball downfield and Darren Bent, restored to Fulham's starting line-up after his equaliser at Manchester United on Sunday, neatly laid the ball off to Tunnicliffe.
Rene Meulensteen's side gained encouragement from their start and centre-back Dan Burn came close to breaking the deadlock when he rose highest to Lewis Holtby's corner.
Then the visitors fell behind in the eighth minute in the worst possible fashion as Ivory Coast defender Toure sliced his clearance into the back of the net.
Holtby produced a slick pass beyond Skrtel and Richardson's cross was shinned home by the Ivorian centre-back.
It was the second mistake by Toure this month following his howler which gifted West Bromwich Albion a share of the spoils at the Hawthorns on February 2.
The hosts received a sudden shot of confidence and Holtby shot wide only a couple of minutes later.
Liverpool finally produced an attack of note in the 13th minute when Luis Suarez's shot was turned around the post by Maarten Stekelenburg.
But there was nothing the Dutch goalkeeper could do four minutes before half-time when Gerrard sliced the Fulham defence open with a superb outside of the boot pass and Sturridge raced clear, steadied himself and then curled the ball home left-footed off the far post.
Suarez had three chances early in the second period, the latter crashing against the outside of the post.
Yet Liverpool were let down once again by poor defensive work as Richardson fired the home side ahead from close-range in the 63rd minute.
Riether's cross from the right did not look dangerous until Skrtel took the ball away from John Flanagan and his sliced intervention landed into the path of Richardson, who slotted past Mignolet from three yards out.
But that was not to deter Liverpool in an entertaining and enthralling contest.
Coutinho collected Sturridge's pass on the edge of the box and surged in field.
His shot did not appear like it would threaten Stekelenburg, but a deflection off Johnny Heitinga did enough to beat the former Ajax stopper as the ball nestled into the bottom corner.
Stekelenburg had to be replaced when Suarez's foot collided with his head and Liverpool eventually found a way past his replacement David Stockdale.
Sturridge was fouled by Riether and Gerrard sparked wild celebrations among the travelling faithful behind Stockdale's goal with the calmly converted penalty.
What the stars mean:
★ Poor ★ ★ Promising ★★★ Good ★★★★ Very good ★★★★★ Exceptional