Most of the pre-match headlines before this game were dominated by confirmation that Andrew Robertson would be leaving at the end of the season, and he was one of the Reds who had an early opportunity.
His strike from the edge of the area was heroically blocked by Harry Wilson, just moments before another end-of-season departure in Mohamed Salah stung the palms of Bernd Leno when he struck from a tight angle.
Pressure was building on the Fulham goal and it almost told after 20 minutes when Cody Gakpo whistled an effort inches wide of the post from the edge of the area.
The Cottagers grew into the half and looked more threatening as it went on, testing Giorgi Mamardashvili in the Liverpool goal twice in quick succession when Alex Iwobi and Oscar Bobb forced the Georgian stopper into smart saves, moments before Harry Wilson curled an effort onto the roof of the net.
They were left to rue those missed chances before half-time, when Rio Ngumoha twisted and turned inside the area before nestling home a sumptuous curling effort into the far corner.
Salah compounded Fulham’s misery before the break too, sweeping home in almost identical circumstances to leave Marco Silva’s men with a mountain to climb after the break.
He reacted by making a double switch at half-time, introducing Sasa Lukic and Emile Smith Rowe, and the former of the duo had the ball in the back of the net within five minutes of the restart, only he’d strayed a few yards offside in doing so.
Fulham had their moments in front of goal, creating another gilt-edged opportunity from a set piece, as the unmarked Rodrigo Muniz saw his goalbound header diverted away to safety by Florian Wirtz.
The London outfit continued to probe from corners, spurning another chance when Joachim Andersen climbed highest at the far post but could only divert Wilson’s delivery just wide of the post.
Smith Rowe had a glorious chance to halve the arrears when he turned wide from six yards out, and that proved to be Fulham’s last big chance of the game as they slumped to a ninth away league defeat of the season.
Things look brighter for Liverpool, who prepared for their midweek UEFA Champions League game against PSG in the best possible fashion, where they’ll need a repeat scoreline to have any chance of progressing.