The Cottagers showed intent from the very beginning and Andreas Pereira forced a mistake from Ibrahima Konaté in his own box, although Rodrigo Muniz was halted by Virgil van Dijk when the ball was slid across.
The hosts still found themselves behind in the 14th minute, as Ryan Gravenberch regained possession and Alexis Mac Allister strode forward before firing an outrageous strike from range out of Bernd Leno’s reach.
Undeterred by that setback, Fulham continued to compete and were rewarded just nine minutes later. Pereira’s cross was unconvincingly dealt with by Curtis Jones, and Ryan Sessegnon pounced to clinically finish on his first PL start at Craven Cottage since May 2019.
Andrew Robertson then appeared to have got away with a sloppy square pass when Konaté blocked Alex Iwobi’s shot, but the left-back’s moment of calamity continued when he headed the ball back to the Nigeria international, then deflected his shot past Caoimhín Kelleher.
The rampant Cottagers had another just five minutes later, with Muniz superbly holding off Van Dijk and controlling Iwobi’s looped ball before firing through Kelleher’s legs.
Liverpool showed more urgency after the restart, but Leno rushed out to deny Diogo Jota after Mohamed Salah had dispossessed Calvin Bassey and Dominik Szoboszlai’s attempt trickled wide.
Arne Slot took action with a double change in the 55th minute, but there was no immediate change to the pattern of play as Robertson struck over, a timely Gravenberch block was required to deny Pereira at the other end, while Salah’s shot sailed over the crossbar.
Another round of substitutions brought the change the Reds craved, as Conor Bradley was introduced and raced forward before laying the ball off for Luis Díaz to finish.
They still couldn’t quite draw level though, with Harvey Elliott hitting the crossbar before he and Federico Chiesa both saw an attempt held by Leno, as Fulham responded to their back-to-back defeats with a brilliant victory that keeps prospects of a European adventure tantalisingly within reach.
While Liverpool are close to their own goal of securing the PL title, the Reds will want to end their stuttering form having lost three of their last four across all competitions.
Flashscore Man of the Match: Rodrigo Muniz (Fulham)