Match ends, Liverpool 4, Everton 0.
Liverpool stretched their unbeaten run against Everton at Anfield to 17 years with an eye-catching performance in Jurgen Klopp's first Merseyside derby.
The Reds impressed against the lacklustre Toffees who also had Ramiro Funes Mori sent off.
Divock Origi headed his side into the lead, with Mamadou Sakho scoring a second.
Daniel Sturridge drove in a third before Philippe Coutinho's curled finish completed an emphatic win.
The result keeps Liverpool in with an outside chance of a top-four finish. They are seventh on 54 points, six points behind Arsenal in fourth while Everton are 11th on 41 points.
A tale of two teams
Everton have not won at Anfield since 1999 and, in truth, they never looked like getting anything from their latest visit.
The Reds looked more organised from the outset, attacked with pace and in numbers, and only a couple of good saves from Joel Robles prevented the hosts from taking the lead much earlier than the 43rd minute.
The sending-off of Funes Moris, after he stood on Origi's ankle, arguably ended any hopes of an Everton fightback but there had been little to suggest that was ever on the cards.
Liverpool finished with 37 shots on goal, 13 of those on target, while all three of Everton's efforts were wide.
This was the 226th Merseyside derby and one of the most one-sided but it did come at a cost for Liverpool as Klopp confirmed Origi had twisted his ankle.
Pressure mounting on Martinez?
The first Merseyside derby this season proved to be the final game in charge for Klopp's predecessor Brendan Rodgers.
Pressure had been mounting on the 43-year-old after a disappointing start to the season in which the Reds had won just three of their opening 10 games and, after a 1-1 draw at Goodison on 4 October, he was sacked.
The situation Rodgers found himself in before his departure mirrored Roberto Martinez's going into this game. The Everton boss was under pressure to get a positive result on Wednesday, having overseen just three wins in the 10 games prior to the trip to Anfield.
That pressure now shifts to Everton's next game, with Martinez needing to pick up his players for an FA Cup semi-final with Manchester United at Wembley on Saturday.
Klopp's magic touch
Since Klopp arrived at Liverpool shortly after Rodgers' departure, the transformation of some of the club's once-out-of-favour players has been impressive.
Origi was sent out on loan to Lille last year and failed to shine as he was named in L'Equipe's worst Ligue 1 team of the season, while Sakho found himself a peripheral figure at Liverpool in the latter stages of Rodgers' reign.
Both, though, have become important parts of a Liverpool side that have now won four straight games games in all competitions - including last week's impressive victory over Borussia Dortmund in the Europa League.
Just as on that night, both Origi and Sakho scored against Everton while Lucas Levia, who almost left the club at the start of this season, provided the assist for Sturridge's goal.
On top of that, Klopp was able to make nine changes from the side that beat Bournemouth 2-1 at the weekend. The former Dortmund boss has found a way to get the best out of the players in his squad.
What they said
Liverpool manager Jurgen Klopp: "It was really difficult for Everton: red card, injuries, good opponent.
"The second half changed completely with the red card and then the next change when John Stones had to come off that was really not easy for Everton.
"There was no real fight any more. That is not usual. There have been a lot more intensive derbies for sure and there will be a lot more intensive derbies."
Man of the match - James Milner
The stats you need to know
- There have now been 21 red cards in the Merseyside derby in Premier League history, more than any other fixture (14 Everton, 7 Liverpool).
- Daniel Sturridge has scored more goals in the Premier League against Everton than against any other team (6).
- Divock Origi has scored five times in his past five games for Liverpool (all competitions).
- James Milner has recorded 11 assists in 2016 in all competitions, three more than any other Premier League player.
- Liverpool have won back-to-back games at Anfield in the Premier League for the first time since May 2015.
- Liverpool are unbeaten in the past 11 Premier League Merseyside derbies (W4 D7 L0).
- Everton's two heaviest Premier League Merseyside derby defeats have both been under Roberto Martinez and both at Anfield (4-0 in January 2014)
Liverpool host relegation-threatened Newcastle on Saturday while Everton play Manchester United in the FA Cup semi-finals.
- 7MilnerBooked at 8minsSubstituted forIbeat 81'minutes
- 11FirminoSubstituted forAllenat 66'minutes
- 27OrigiSubstituted forSturridgeat 54'minutes
- 4K Touré
- 44B Smith
- 5StonesSubstituted forPienaarat 62'minutes
- 25Funes MoriBooked at 50mins
- 18BarrySubstituted forBesicat 45'minutes
- 20BarkleySubstituted forCleverleyat 58'minutes
- 12LennonBooked at 42mins
- Robert Madley
- Shots on Target
Second Half ends, Liverpool 4, Everton 0.
Foul by Alberto Moreno (Liverpool).
Aaron Lennon (Everton) wins a free kick in the defensive half.
Attempt saved. Daniel Sturridge (Liverpool) left footed shot from outside the box is saved in the top left corner. Assisted by Philippe Coutinho.
Offside, Liverpool. Adam Lallana tries a through ball, but Daniel Sturridge is caught offside.
Corner, Liverpool. Conceded by Joel Robles.
Attempt missed. Lucas Leiva (Liverpool) right footed shot from outside the box is close, but misses to the left. Assisted by Alberto Moreno.
Attempt missed. Nathaniel Clyne (Liverpool) right footed shot from the centre of the box is too high. Assisted by Adam Lallana with a through ball.
Attempt saved. Jordon Ibe (Liverpool) left footed shot from outside the box is saved in the centre of the goal. Assisted by Nathaniel Clyne.
Foul by Jordon Ibe (Liverpool).
Bryan Oviedo (Everton) wins a free kick in the defensive half.
Joe Allen (Liverpool) wins a free kick in the defensive half.
Foul by Steven Pienaar (Everton).
Attempt missed. Alberto Moreno (Liverpool) left footed shot from outside the box is too high. Assisted by Philippe Coutinho following a corner.
Corner, Liverpool. Conceded by Leighton Baines.
Attempt missed. Alberto Moreno (Liverpool) left footed shot from outside the box is high and wide to the left. Assisted by Adam Lallana following a corner.
Corner, Liverpool. Conceded by Leighton Baines.
Hand ball by Bryan Oviedo (Everton).
Substitution, Liverpool. Jordon Ibe replaces James Milner.