Brendan Rodgers's improving team overpowered feeble Fulham at Anfield to ascend to eighth place in the Premier League, their goals coming from Martin Skrtel, Steven Gerrard, Luis Suárez and, most handsomely, Stewart Downing, who was back to England form.
Liverpool were in charge from the first minute to the last against bedraggled opposition, who defended in abject fashion and have won only one of their past 10 Premier League matches.
Rodgers was delighted with his players' reaction after last week's 3-1 defeat at home to Aston Villa and singled out Downing for individual praise. He revealed having "an honest conversation" with the player "a little while ago", during which he had threatened to offload him in January.
The manager said: "I pointed out that he was an England player two years ago and if he couldn't get in our team this season it was time for him to move on. Since that conversation his response has been quite outstanding. I thought he was brilliant in every aspect of his game and if he keeps playing like that he'll be going nowhere."
Fulham were dreadful. Martin Jol said: "We need more conviction" and there will be a few Cottagers more than willing to convict after this. The poverty of their performance was such that the margin would have been doubled but for some notable second-half saves by Mark Schwarzer, especially to deny Suárez.
Fulham had lost the previous weekend against QPR, and switched from 4-4-2 to 4-2-3-1, discarding a striker, Hugo Rodallega, in the process. Jol was also without Steve Sidwell and Mahamadou Diarra in midfield, and sought security by deploying Kieran Richardson and Chris Baird as a two-man screen in front of his back four.
That security lasted eight minutes. Then Gerrard's corner from the right fell nicely for Skrtel, beyond the penalty spot, to thrash it, right-footed, into the roof of the net. Downing quickly threatened to improve Liverpool's lead with a pulverising 25-yarder that Schwarzer, flying to his left, clearly saved, only for Mark Clattenburg to award a goal-kick.
Fulham tried to play their customary passing game but in the absence of Sidwell and Diarra they struggled for possession and the only surprise about the second goal was that it was delayed until the 36th minute. Then a characteristic run by Gerrard was picked out by Downing's lovely reverse pass, the England captain finishing with accurate aplomb, from right to left.
Suso, supplied by Suaréz, ought to have made it 3-0 before half-time, but screwed his shot horribly wide.
Jol introduced Rodallega at the start of the second half and reverted to 4-4-2 but Liverpool resumed where they had left off and within two minutes they should have had their third, Suárez of all people failing to score at the far post from Downing's inviting cross. No matter, Downing promptly demonstrated how such things should be done, cutting in from the right on to his left foot and letting fly at a velocity that left Schwarzer powerless to intervene.
Trailing by three with 51 minutes played, Fulham were in danger of a real hiding. Glen Johnson was too close for Schwarzer's comfort and Downing inches over from 25 yards. The outcome long since settled, Rodgers sent on Raheem Sterling to receive the applause of a crowd delighted that the precociously gifted 18-year-old had signed a five-year contract. An even bigger cheer greeted the introduction of the old warhorse Jamie Carragher. By this stage Rodgers could easily afford to play Santa Claus.
Rodallega had Pepe Reina at full stretch in added time but Liverpool had the last word, Suárez getting in on the act with a crisp finish from six yards.