Mario Lemina’s goal on the stroke of half-time proved decisive at Anfield, where an improved display from the Reds after the break saw Sadio Mane go closest to an equaliser.
The No.10 came off the bench and hit the woodwork with a header but, despite the application of concerted pressure on Fulham in the final stages, Jürgen Klopp’s side could not find a way through and slipped to a sixth successive home loss.
Team news
Klopp made seven changes to his starting XI, with Diogo Jota returning.
With Roberto Firmino sidelined due to a minor knock and Mane among the substitutes, Xherdan Shaqiri joined Jota and Mohamed Salah in attack.
Naby Keita and James Milner started in midfield, while Nathaniel Phillips, Neco Williams and Rhys Williams came in at the back.
First half
An early shout for a penalty when Salah - who was deployed centrally, flanked by Shaqiri on the right and Jota on the left - appeared to be blocked off by Ola Aina was waved away by referee Kevin Friend.
Almost immediately, Josh Maja volleyed Ivan Cavaleiro’s cross wide at the other end, before Ademola Lookman cut inside off the left flank and failed to beat Alisson Becker at his near post.
A speculative Salah half-volley on the swivel from outside the area didn’t trouble Alphonse Areola, but Alisson had to be alert to smother the ball at Maja’s feet as Fulham continued to look dangerous.
Milner then flashed a rising, left-footed strike narrowly over the crossbar, though Liverpool were again indebted to Alisson when the Brazilian repelled Lookman’s effort from point-blank range.
However, after Shaqiri had sent a dipping free-kick onto the roof of Areola’s net, the visitors got their goal in the final minute of the half when, in the aftermath of a corner, Lemina dispossessed Salah and smashed home a low drive across Alisson.
Second half
There was a significantly greater intensity about the Reds’ work straight after the restart, and a moment of real class from Jota almost saw them level with 48 minutes on the clock.
Neco Williams delivered from the right and Jota acrobatically crashed an instinctive volley goalwards, only for Areola to palm it away.
Fulham retained a threat on the counter-attack, though, and Phillips was required to intelligently thwart Lookman before Klopp looked to his bench for inspiration.
Mane replaced Georginio Wijnaldum on the hour and hit the woodwork 10 minutes later, the forward leaping prodigiously to arc a header over the stranded Areola and back off the angle of post and bar.
Shaqiri, seeking the top corner, curled a fraction wide from 20 yards as Liverpool’s urgency grew, with Klopp then sending Trent Alexander-Arnold and Fabinho on with a touch under 15 minutes remaining.
Alexander-Arnold’s first involvement of note saw him deliver a deep cross to Mane, but the Senegalese miscued his header into the ground.
Mane then appeared certain to score in stoppage time, only for a defender to get to Andy Robertson’s low ball ahead of him to leave Liverpool frustrated again.