The hosts tested the water early on when a Curtis Jones shot was saved by Bernd Leno, but it was the Cottagers that broke the deadlock with their first sniff of a chance.
Willian beautifully weaved his way through the box and fired a clinical strike past Caoimhin Kelleher after Virgil van Dijk misjudged the flight of the ball and allowed Andreas Pereira to tee up his compatriot.
Jurgen Klopp cut an increasingly frustrated figure amid the backdrop of a subdued Anfield, as Van Dijk was shown a harsh yellow card for colliding with Pereira before the German was left fuming again when referee David Coote did not play advantage after a foul on Alexis Mac Allister.
Joe Gomez aimed to restore parity on his 200th Liverpool appearance but shot wide from distance just seconds before half time.
It was almost one-way traffic after the break, with Ryan Gravenberch firing wide after weaving his way into a shooting position before Antonee Robinson made a fine block to keep out Diogo Jota’s effort.
Klopp bolstered his attack by introducing both Cody Gakpo and Darwin Nunez in place of Gravenberch and Harvey Elliott in a bid to break down a stubborn Fulham defence.
Marco Silva’s side were looking for a second goal on the counter-attack, but Bobby Decordova-Reid went for glory down the right-hand side despite Pereira being unmarked inside the box.
Liverpool managed to get the goal which they felt their pressure deserved, in hugely unfortunate circumstances from a Fulham perspective.
Jones took aim from the edge of the area and saw his strike take a huge deflection off Tosin Adarabioyo before beating Leno.
While there may have been an element of fortune about the equaliser, Liverpool’s attacking prowess came to the fore for their second moments later.
Jota and Nunez combined brilliantly to tee up Gakpo for a clinical finish at the near post, as Silva’s men saw their advantage wiped out in a mere four minutes.
It would prove to be a telling blow and another ominous sign to Liverpool’s rivals after Klopp’s men secured another victory without being at their free-flowing best.
The Reds are now unbeaten in their last seven games across all competitions since a 2-1 dead-rubber UEFA Europa League defeat to Royale Union Saint-Gilloise last month.
As for Fulham, this is another near-miss on Merseyside having pushed Klopp’s men close after losing this Premier League fixture 4-3 on December 3rd.
Silva’s men are still firmly in the tie though heading into the second leg at Craven Cottage on January 24th.
Flashscore Man of the Match: Curtis Jones (Liverpool)
