In one of the showpiece fixtures of the season under the lights at Anfield, the game lived up to its billing in an extraordinary first half which saw six goals scored.
Sadio Mane laid on two sublime assists for Divock Origi (6) and Xherdan Shaqiri (17) - who were both handed starts in place of Mohamed Salah and Roberto Firmino - to put Liverpool in control.
Michael Keane (21) hit back for Everton but two more special Liverpool goals from Origi (31) and Mane (44) restored the three-goal cushion for just two minutes before Richarlison (45+2) made it 4-2 just before the break.
It is now 20 games unbeaten for Liverpool against Everton in all competitions and under-pressure Toffees boss Marco Silva now sees his team in the relegation zone after losing nine of their last 13 Premier League games.
Following the defeat Silva is on the brink of losing his job, according to Sky Sports News.
With a home game to come against Frank Lampard's Chelsea on Saturday, the atmosphere at Goodison Park could be toxic and it is likely majority shareholder Farhad Moshiri will not want to put Silva into that environment.
Liverpool: Adrian (7), Alexander-Arnold (7), Van Dijk (7), Lovren (8), Robertson (8), Wijnaldum (8), Milner (7), Lallana (7), Mane (9), Origi (9), Shaqiri (8)
Subs: Henderson (7), Firmino (N/A), Gomez (N/A)
Everton: Pickford (5), Digne (5), Sidibe (5), Holgate (5), Keane (5), Mina (4), Davies (4), Sigurdsson (5), Iwobi (4), Richarlison (7), Calvert-Lewin (6)
Subs: Bernard (6), Kean (5)
Man of the match: Sadio Mane
- 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.
- Everton find themselves in the relegation zone after playing at least 15 Premier League matches for the first time since April 10th 1999 (after 32 games).
- Silva is the first Everton manager to concede five league goals against Liverpool in a single match since Howard Kendall in November 1982 (0-5 against Bob Paisley's Liverpool).
Next up for Liverpool is a visit to Bournemouth on Saturday followed by a trip to Red Bull Salzburg on Tuesday in the Champions League. Meanwhile, Everton host Chelsea on Saturday lunchtime.