Sadio Mane created goals for Xherdan Shaqiri and Divock Origi, who bagged a brace at Anfield. Mane also added one himself, while Georginio Wijnaldum ended the scoring in the final minute to help the Reds stay eight points clear of Leicester City at the top of the table.
Liverpool barely needed six minutes to punish their struggling neighbours, going in front when Mane rolled an inch-perfect pass into the path of Origi. The man drafted in to give Roberto Firmino a rest coolly rounded Everton goalkeeper Jordan Pickford before passing the finish into the net.
Origi has made it a happy habit to score against the Toffees:
Origi's latest derby goal was made by Mane's vision and technique, and the Senegal international was the creator again when he played in Shaqiri to double the Reds' tally 11 minutes later.
Shaqiri, like Origi, was a surprise selection, one affording Mohamed Salah the chance of a break. The Swiss winger had vindicated Jurgen Klopp's decisions.
Liverpool appeared to be coasting, but the league leaders' recent vulnerability at the back showed itself again when Keane found space in the box to sweep in an unlikely goal against the run of play, following a scramble from a corner:
Fortunately for Klopp, his team is never short of goals. The third came from an unlikely route, when Dejan Lovren lifted a pass over the top for Origi, who collected it with a deft touch before lobbing Pickford for his fifth derby goal.
Beleaguered Everton boss Marco Silva responded by brining on Brazil international forward Bernard in place of right wing-back Djibril Sidibe. The latter had struggled mightily to keep Mane in check, but BBC Sport's Phil McNulty felt the tactical reshuffle had come too late:
Changes in shape and personnel did little to improve the Toffees' fortunes, with Liverpool soon cashing in to score a fourth. Fittingly, Mane got the goal, but only after superb work from Trent Alexander-Arnold, who broke clear and picked out the free-scoring No. 10 to cap his first-half masterclass.
Liverpool were irresistible going forward, but those familiar failings at the other end of the pitch wouldn't go away. Richarlison made it 4-2 on the stroke of the break when he met Bernard's cross with the combination of his head and shoulder.
The late goal made for a strange atmosphere after the restart, with an underlying current of nerves among the home faithful. Those nerves were justified when Keane headed at Adrian from a corner, while the Spaniard had to be quick off his line to deny Richarlisonanother chance.
A snap-shot from Tom Davies fell kindly for the man in the Liverpool goal, but it did offer a reminder of Everton's enduring threat. The Toffees were causing problems whenever they launched deep crosses into the box, with confusion common between Virgil Van Dijk and Lovren.
In truth the game had fallen flat, with the pace of play sluggish and quality in possession lacking from both sides. Even so, Mane spurned two excellent chances to add to his tally, while Everton substitute Moise Kean failed to close the gap after being played clean through.
There was still time for Liverpool to offer Kean and the Toffees a lesson in ruthless finishing when Wijnaldum profited from fine work by sub Firmino.
It was a fitting way for the Reds to cap what had been a performance typifying their strength this season. There isn't a more powerful team going forward, even if Klopp will be keen to plug the recurring gaps in defence.