Match ends, Liverpool 5, Everton 2.
Liverpool pushed Everton manager Marco Silva closer to the sack and retained their eight-point lead at the top of the Premier League with a crushing win at Anfield which dropped the Toffees into the relegation zone.
Reds boss Jurgen Klopp, already missing suspended goalkeeper Alisson and injured Fabinho, still felt able to rest key attacking duo Mohamed Salah and Roberto Firmino from his starting line-up and win in comfort.
Liverpool effectively won the game with four goals in the first half - Sadio Mane creating two early strikes for Divock Origi and the recalled Xherdan Shaqiri.
Michael Keane pulled one back for shambolic Everton but Liverpool were soon back in control when Origi controlled Dejan Lovren's pass for a brilliant third and Mane got the goal he deserved when he crowned a sweeping counter-attack from Trent Alexander-Arnold's inviting delivery.
Richarlison took advantage of Liverpool's own vulnerable defending to make it 4-2 on the stroke of half-time but in reality Everton were never seriously in contention at any point.
Both sides missed chances in the second half, with the brilliant Mane and Everton substitute Moise Kean culprits, but Liverpool completed the humiliation for Silva and his team with Georginio Wijnaldum's low shot for the fifth in the final minute of normal time.
The question now, as Everton lie in the bottom three, is how long the beleaguered Silva can survive, with Chelsea scheduled to visit Goodison Park on Saturday lunchtime.
- 'I don't have the answer' - Everton boss Silva says his future is uncertain after derby defeat
- Football Daily: Divock's derby delight & Rashford ruins Mourinho's night
Silva under siege
Silva, 42, is suffering a slow, lingering demise as Everton manager - and this dismal showing is only likely to hasten his exit from Goodison Park.
This was a Liverpool side nowhere near full strength but the game was up for Silva and Everton once they were two down inside 17 minutes.
Silva's five-man defensive system was ripped to shreds, by Mane in particular, and it was no surprise when he removed defender Djibril Sidibe before half-time to introduce Brazilian attacker Bernard.
Everton were a team in chaos at times in the first half, with Sidibe, Mason Holgate, Tom Davies and Keane all arguing among themselves after Shaqiri's goal then Holgate and Lucas Digne also in animated discussion after Origi put Liverpool 3-1 up.
Director of football Marcel Brands cut a concerned figure at half-time, deep in discussion with fellow director Sasha Ryazantsev - and there will surely be more discussions among the Everton hierarchy post-match.
Everton did create some chances but never looked like ending a winless Anfield sequence stretching back to September 1999.
It is also the first time Everton have conceded four goals in the first half of a Merseyside derby since 1935.
Silva now faces an uncertain future - and Everton face what increasingly looks like a relegation fight.
Liverpool march relentlessly on
Liverpool continue their relentless march towards what will be a first league title for 30 years and this victory was a graphic illustration of the strength at manager Klopp's disposal.
It was Klopp's 100th Premier League victory - he is the second-fastest manager to reach a century in the competition - and it extends the Reds' run of 32 matches without defeat, their longest such run in top-flight history.
Liverpool, who lost only one Premier League game since the start of last season, were not even at full tilt or full strength and yet eventually overwhelmed their struggling Merseyside neighbours.
Salah was able to have the night off and Firmino and captain Jordan Henderson were only introduced as late substitutes as Klopp rotated his resources.
Liverpool's defence was vulnerable but their sheer potency in attack more than compensates, led by the world-class Mane, who tormented Everton all night and only blotted his copybook by missing two chances to make the scoreline even more emphatic.
And Origi is fast becoming Everton's bogeyman, scoring twice in the first half after grabbing that dramatic 96th-minute winner in this same fixture last season.
Liverpool were nowhere near their best, not that they needed to be, but this was an impressive demonstration of the power assembled by Klopp that has put them in such a commanding position in the title race.
Man of the match - Sadio Mane
A flashback to 20 years ago - the best of the stats
- Everton find themselves in the relegation zone after playing at least 15 Premier League matches for the first time since April 1999 (after 32 games).
- Liverpool are unbeaten in their past 32 Premier League games (W27, D5), their longest ever run without defeat in top-flight history.
- Klopp has won 100 of his 159 Premier League games, he is the second fastest manager to reach 100 wins in the competition, after Jose Mourinho (142 games). In fact, he is the fastest Liverpool manager to 100 wins in top-flight history.
- Liverpool are unbeaten in their past 18 Premier League games against Everton (W8, D10). It's their longest ever unbeaten run against a specific opponent in the competition.
- Silva is the first Everton manager to concede five league goals against Liverpool in a single match since Howard Kendall in November 1982 (5-0 against Bob Paisley's Liverpool).
- Since the start of last season, Trent Alexander-Arnold has provided more Premier League assists than any other player (18), with 15 of those coming in 2019.
'I loved it a lot!' - what they said
Liverpool manager Jurgen Klopp, speaking to Match of the Day: "All the goals were incredible, outstanding. Wonderful goals, sensational passes, super pieces of football. I loved it a lot!
"We needed fresh legs and I had to show my respect to the boys in the squad, that's all. They proved it. It is much more fun making changes, all of the boys are ready to deliver performances like this.
"It was a massive moment in my first season when Divock Origi got injured in the derby. It changed his career for a bit."
Everton boss Marco Silva, speaking to Match of the Day: "We cannot concede goals in the way we conceded. We knew everything about them before the match and how they like to play whether with Origi, Salah or Firmino, we know how they would play. There was a lot of mistakes.
"I am not the right person to answer about the situation, this question is for different people. We are making some mistakes which put us under big, big pressure. The type of mistakes we are making is because the players are playing under big pressure because of the position in the table."
Liverpool travel to Bournemouth on Saturday for another Premier League match (15:00 GMT), while Everton host Chelsea in the early kick-off on the same day (12:30).
- 66Alexander-ArnoldBooked at 27minsSubstituted forGomezat 83'minutes
- 4van Dijk
- 20LallanaSubstituted forHendersonat 72'minutes
- 27OrigiSubstituted forFirminoat 73'minutes
- 19SidibéSubstituted forBernardat 35'minutes
- 26DaviesBooked at 67minsSubstituted forSchneiderlinat 72'minutes
- 10G Sigurdsson
- 7RicharlisonBooked at 31mins
- 9Calvert-LewinSubstituted forKeanat 60'minutes
- Mike Dean
- Shots on Target
Second Half ends, Liverpool 5, Everton 2.
Goal! Liverpool 5, Everton 2. Georginio Wijnaldum (Liverpool) right footed shot from the centre of the box to the bottom right corner. Assisted by Roberto Firmino.
Corner, Liverpool. Conceded by Lucas Digne.
Attempt blocked. Xherdan Shaqiri (Liverpool) left footed shot from outside the box is blocked. Assisted by Georginio Wijnaldum.
Dejan Lovren (Liverpool) wins a free kick in the defensive half.
Foul by Richarlison (Everton).
Attempt missed. Moise Kean (Everton) right footed shot from outside the box is close, but misses to the left. Assisted by Alex Iwobi with a through ball.
Corner, Everton. Conceded by Georginio Wijnaldum.
Substitution, Liverpool. Joseph Gomez replaces Trent Alexander-Arnold.
Foul by Jordan Henderson (Liverpool).
Gylfi Sigurdsson (Everton) wins a free kick in the attacking half.
Offside, Everton. Lucas Digne tries a through ball, but Richarlison is caught offside.
Attempt missed. Sadio Mané (Liverpool) right footed shot from the centre of the box is close, but misses to the right. Assisted by Jordan Henderson with a through ball.
Corner, Everton. Conceded by James Milner.
Foul by James Milner (Liverpool).
Mason Holgate (Everton) wins a free kick in the defensive half.
Attempt missed. Georginio Wijnaldum (Liverpool) header from the centre of the box is too high. Assisted by Xherdan Shaqiri with a cross following a set piece situation.
Sadio Mané (Liverpool) wins a free kick on the left wing.
Foul by Morgan Schneiderlin (Everton).