Liverpool delivered a first-half masterclass to humiliate Everton at Anfield on Wednesday, surging into a 4-2 halftime lead and adding a late fifth to maintain their charge towards a first league title in 30 years.
Rarely in that barren period, or even in the glory years that preceded it, could they have produced a better first half as exquisite passing and deadly finishing brought two goals for Divock Origi and one each for Xherdan Shaqiri and Sadio Mane.
Everton replied through Michael Keane and Richarlison before a much calmer second half that brought only a late goal for Georginio Wijnaldum.
The victory, coach Jurgen Klopp's 100th in the Premier League in the highest-scoring Merseyside derby for 86 years, made it a top-flight club record of 32 league matches unbeaten for Liverpool.
It moved the European champions on to 43 points, eight ahead of Leicester City, who beat Watford earlier, and 11 clear of Manchester City.
For Everton, who have not won at Anfield since 1999, the defeat made it 20 derbies in all competitions without a victory home or away and dropped them into the Premier League's bottom three, with the pressure piling up on manager Marco Silva.
"The manager showed trust and you just have repay it," said Origi. "I think my first goal was important to break the game open, but the second one, technically, I enjoyed. We used the space well. We had wonderful service."
What Silva would give for a reserve striker like Origi, who came in to score two great goals.
After six minutes, the Belgian was the beneficiary of a wonderful pass by Mane, who curved the ball perfectly between the retreating Mason Holgate and advancing goalkeeper Jordan Pickford, allowing Origi to take a touch beyond both and knock it into the empty net.
Trent Alexander-Arnold then delivered another stunning pass, drilled 40 yards cross-field into the path of Mane, who nonchalantly controlled it and put it on a plate for Shaqiri.
Everton pulled one back four minutes later through Michael Keane but he and his defensive partners were exposed again soon after when a simple long ball by Dejan Lovren found the unmarked Origi, who cushioned the ball expertly before firing home.
Liverpool then scored yet another brilliant goal, Mane breaking at pace from his own box, moving the ball to Alexander-Arnold, who fed the ball back to the galloping Senegalese striker to clip in a superb low shot from the edge of the box.
After a much calmer second half saw Mane and Everton's Moise Kean both miss late chances, Wijnaldum completed the rout in the highest-scoring Merseyside derby since Liverpool won 7-4 in 1933.