Two goals down within the opening half hour, they somehow found a way to win, ultimately comfortably, with the help of an own goal and a deflected free-kick and despite being reduced to 10 men in the second half.
Rafael Benitez could regard himself as particularly fortunate since he had got his selection hopelessly wrong with the omission of Xabi Alonso from his starting line-up. But like all good managers he acknowledged his mistake and rectified it, bringing on the diligent and inventive Spanish midfielder at half-time with damaging consequences for Fulham.
The west London club would appear to be further down the road towards a much-needed takeover than Liverpool, despite the denials of Mohamed Fayed, yet one would never have guessed just how much in need of a fresh cash injection they are on yesterday's first-half performance.
On paper, the Cottagers looked desperately threadbare yesterday, all the more so thanks to the unnecessary suspensions of Andy Cole and Ian Pearce, but Chris Coleman, the manager, had called for a show of greater discipline and his players answered it.
For all their lively start, Liverpool had only ever looked dangerous when Milan Baros was almost put through, but a crunching blocked tackle from the imposing Zat Knight put paid to that.
Only an acrobatic hooked clearance from Sami Hyppia prevented Fulham breaching the Liverpool defence in the 23rd minute. It was an early warning. A minute later Salif Diao made his second mistake within seconds with a careless backheel and was severely punished for it, Boa Morte turning in Brian McBride's cross.
Defender John Arne Riise then went closest for Liverpool in the first half with a header, but Fulham were temporarily a team inspired and if the build-up were somewhat fortuitous the finish by Boa Morte to Steve Malbranque's through ball was emphatic, the Portuguese firing through the legs of Chris Kirkland.
Liverpool's hopes of getting quickly back into this match in the second half were assisted in the most bizarre fashion three minutes after half-time when a hopeful cross from Baros struck Knight on the chest and the ball bounced over the head of Edwin Van der Sar in the home goal.
The goal lifted Liverpool, who, not surprisingly, had brought on Alonso at half-time for the hapless Diao. In their eagerness to right the wrongs of the first half, however, they overstepped the mark and three players - Josemi, Luis Garcia and Djimi Traore - were booked in the first 15 minutes.
The impetus, nevertheless, was now clearly with the away team and after 70 minutes they drew level. A cross by Alonso was met perfectly by the head of his fellow Spaniard Garcia and although Van der Sar parried it he could do nothing to prevent Baros from scoring on the rebound. The struggling Josemi then handed the initiative back to Fulham when he transgressed again with a foul on Boa Morte and was sent off.
No matter. Within two minutes Liverpool were ahead when a free-kick by Alonso from more than 25 yards took a deflection off the head of Pape Boa Morte, completely wrong-footing Van der Sar. A fourth goal from Igor Biscan in injury time merely added insult to injury.