The win over Manchester United moved the Reds two points clear at the top of the table.
In an emphatic performance, the trio of Luis Diaz, Mohamed Salah and Sadio Mane scored the first three goals, two of them in the first 22 minutes, and United simply had no answer.
With his second of the night, Diogo Jota set up by Mo Salah, the Reds added a four-goal win to their five-goal beating of United in October.
United were overwhelmed from the beginning and missed the chance to push for fourth because of the cautious five-man defence.
Liverpool Alisson (7), Alexander-Arnold (7), Matip (7), Van Dijk (7), Robertson (7), Henderson (7), Fabinho (7), Thiago (8), Salah (9), Mane (8), Diaz (8).
Subs: Jota (7), Keita (n/a), Milner (n/a).
Man Utd: De Gea (5), Wan-Bissaka (4), Lindelof (3), Maguire (3), Dalot (4), Jones (4), Pogba (n/a), Matic (4), Elanga (6), Fernandes (4), Rashford (4).
Subs: Lingard (5), Sancho (6), Hannibal (n/a).
Man of the match: Mohamed Salah.
After seven minutes, there was a round of applause for the sad news of the loss of his son.
It was too much for United to compete in the high-tempo game conducted masterfully by Thiago.
The advantage can be restored by Manchester City with a victory over the Seagulls on Wednesday. The quadruple is not going away.
An expectant Anfield did not have to wait long for the breakthrough, as Sadio Mane put Mo Salah away down the right and his cross found the Spaniard who converted from close range.
The first came before the halfway point of the first half, with a sumptuous pass from the provider, and the second came before the end of the half, with a goal from the provider.
The atmosphere was so loud that the half-time whistle gave United some respite.
Jurgen Klopp made only two changes to the Liverpool team that beat Manchester City in the FA Cup semi-final with Joel Matip replacing Ibrahima Konate, while Jordan Henderson was restored in favour of Naby Keita.
Ralf Rangnick made four changes to the Manchester United team that beat Norwich with Aaron Wan-Bissaka, Marcus Rashford, Nemanja Matic and Phil Jones coming in. Alex Telles, Jesse Lingard, Jadon Sancho and Cristiano Ronaldo dropped out.
Phil Jones, making only his second start of the season, was withdrawn in favour of Jadon Sancho at the break as the back five was abandoned.
The goal would have stood even if the assistant had put the flag up earlier.
The hope of a comeback was cut short when Victor Lindelof's pass was picked up by Andy Robertson and he fed the ball to Mane who stroked the ball into the corner of the net.
At that point, the front three had all scored and assisted a goal, but it was Salah who completed the onslaught, Robertson again winning back possession in the build-up.
The Egyptian was very good. They were too good for United.
No team has ever had a longer run without defeat against Manchester United in the competition than the one that lost to them in the last eight games.
Manchester United have conceded the most goals against a team in a single campaign this season, nine against Liverpool. They have conceded more goals against the Reds than any other opponent.
This is the sixth time a team has done the double over Manchester United without allowing a goal, with three of those being responsible for.
Manchester United have lost 9-0 in their two meetings with the Reds this season. In their league history, they only suffered a combined heavier defeat once - 0-11 vs Sunderland in 1892-93.
The first player to score five goals against Manchester United in a single season was Mohamed Salah ofLiverpool.
The only other player to both score and assist in a home and away game against Manchester United in a single season was Mesut zil.
The next assignment for the Reds is in the premier league, where they will face off against their arch rivals at 4.30pm on Sky Sports.
Next up for Manchester United is a trip to the north London stadium to face their rivals.
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