Richarlison's early strike and Gylfi Sigurdsson's penalty earned Everton their first victory at Anfield since 1999 and condemned Liverpool to a fourth successive Premier League defeat.
Richarlison opened the scoring in the third minute after latching onto James Rodriguez's through-ball and finishing in the bottom corner.
Everton had the better chances throughout the first half and Seamus Coleman should have added a second but his diving header was saved by Alisson.
Liverpool suffered another injury blow to one of their stand-in centre-backs as Jordan Henderson limped off after clutching his hamstring with half an hour played.
The Reds improved in the second half but failed to find a way through Jordan Pickford – who had an excellent game for the visitors – and hardly fashioned a clear-cut chance.
And Sigurdsson sealed a historic victory for Everton from the penalty spot after Dominic Calvert-Lewin was felled in the box by Trent Alexander-Arnold on the counter-attack.
The result leaves the two rivals level on points, though the Toffees have a game in hand and have the advantage in the race for a top-four finish.
Here are five talking points from the Merseyside derby.
1. Richarlison gives Toffees dream start
In October's Merseyside derby, Sadio Mane handed Liverpool the perfect start with a third-minute goal at Goodison Park.
At Anfield on Saturday, Richarlison returned the favour with a clinical finish to get Everton off to a flyer.
The Brazilian beat Ozan Kabak for pace to collect James Rodriguez's through-ball and rifle into the bottom corner.
Richarlison also scored in the defeat by Manchester City on Wednesday and has stepped up in the absence of Dominic Calvert-Lewin, who was only fit enough to make the bench after recovering from a hamstring injury.
The Toffees also posed a significant threat thanks to Lucas Digne's delivery from the left wing. Seamus Coleman should have doubled their advantage but was unable to beat Alisson as he met the Frenchman's cross with a diving header.
Everton were arguably more impressive in defence than attack, as Liverpool largely failed to find a way through their visitors and found Jordan Pickford equal to anything he faced on the rare occasions they did get a shot on goal.
The England No.1 made fine saves to deny Jordan Henderson and Mohamed Salah and his positioning and decision making was excellent throughout.
2. Kabak concern
Ozan Kabak's Premier League debut last weekend was marred by his costly mix-up with Alisson which gifted Leicester the lead on their way to a 3-1 victory.
The 20-year-old defender did look much more assured in the 2-0 win over RB Leipzig in midweek and was named man of the match by Liverpool fans.
But against Everton, Kabak endured another shaky display which will call into question his status in Jurgen Klopp's centre-back plans.
Only 10 seconds into the match, the Turk conceded a corner by heading out Everton's punt upfield from the kick-off.
Kabak was also partly at fault for Richarlison's early goal, as his clearing header was collected by the Toffees in midfield before he was beaten by the Brazilian's diagonal run.
He also picked up a yellow card just before half-time for a reckless challenge on Seamus Coleman, taking his tally to three bookings in three games for the Reds.
Kabak moved to Anfield on loan from Schalke in January and his task – to plug the gaping hole in Liverpool's defence – is a mammoth one.
But he will need to show much more composure and a better reading of the game if he is to convince the Reds to activate their option to buy for £18million in the summer.
3. Yet another Liverpool injury blow
With the two injuries Liverpool suffered in the previous Merseyside derby still fresh in the memory, the Reds received yet another blow as Jordan Henderson limped off on the half-hour mark.
Henderson went down clutching his hamstring after shielding the ball from Abdoulaye Doucoure, and was unable to carry on after getting to his feet.
Jurgen Klopp opted to bring on Nat Phillips as the captain's replacement, meaning Liverpool have now had 18 different centre-back partnerships this season.
All of Liverpool's senior options – Virgil van Dijk, Joe Gomez and Joel Matip – as well as emergency back-ups Fabinho and Henderson are now sidelined through injury.
This leaves former Under-23 defender Phillips, youngster Rhys Williams and January signings Ozan Kabak and Ben Davies as Liverpool's available centre-back options.
Klopp desperately needs experience and consistency at this time, but he will have to strike a defensive partnership out of the defensive options at his disposal – or else Liverpool's decline could spiral out of control.
4. Anfield a fallen fortress
After going 68 Premier League games unbeaten at home, Liverpool have now lost each of their last four top-flight matches at Anfield.
The collapse in the Reds' home form has been catastrophic to say the least.
Jurgen Klopp's men used to be invincible on their own turf and a draw for a visiting team was akin to a victory.
But since their near-four-year unbeaten run was shattered by Burnley, they have been defeated by Brighton, Manchester City and Everton.
Liverpool now seem to be just as vulnerable at Anfield as they are on the road and teams are confident of leaving the ground with at least a point.
It seems unlikely Liverpool's home form would have collapsed if fans were present, but Klopp cannot dwell on that; his only concern is getting the Reds back to winning ways at Sheffield United next weekend.
5. Top four in doubt
Having won the Champions League in 2019, Liverpool are now battling to qualify for the competition and find themselves three points adrift of fourth-place Chelsea.
Everton's victory at Anfield means the Merseyside rivals both have 40 points and are separated only by the Reds' superior goal difference, though the Toffees also have a game in hand.
With the top three spots seemingly claimed by Manchester City, Manchester United and Leicester City, the stage is set for a made scramble for fourth place during the run in.
Chelsea will be rueing their failure to claim three points against Southampton earlier on Saturday which means Liverpool, Everton and this season's surprise package, West Ham, are still in touch with the Champions League spots.
Based on current form, Liverpool look the least likely of the current contenders to clinch the final top-four spot.
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