Striker Diogo Jota netted his first hat-trick for Liverpool, as they thrashed Atalanta 5-0 to go five points clear at the top of Champions League Group D, with three straight wins.
Jota's treble continued a scintillating start to his Liverpool career, while Mohamed Salah and Sadio Mane also got on the scoresheet in a superb display from Juergen Klopp's Premier League champions.
Jota wasted an early chance, before giving his side the lead in the 16th minute, latching onto a pass from Trent Alexander-Arnold and holding off Jose Luis Palomino, before delicately flicking the ball past Marco Sportiello.
The Portugal forward, who arrived from Wolverhampton Wanderers for a reported fee of 41 million pounds in September, made it 2-0 in the 33rd minute, controlling a raking pass from Joe Gomez with his left foot, before firing home with his right.
With the home side reeling, Salah scored a super solo goal two minutes into the second half, collecting a clearance from Andy Robertson and running from the halfway line, before curling the ball in at the far post.
Minutes later, Mane made it 4-0 with a sublime chipped finish, before Jota completed his hat-trick with another coolly-taken effort in the 55th for his seventh goal in his first 10 appearances for Liverpool.
Atalanta's best chances on the night fell to Duvan Zapata, who clipped the underside of the crossbar with a superb curling strike. He twice tested Liverpool keeper Alisson with stinging shots and also had a stoppage-time effort ruled out for offside.
Salah almost scored a sixth for Liverpool in the 83rd minute. Once again, he ran half the length of the pitch, after an Atalanta corner was cleared, but this time, his shot was steered out for a corner by Sportiello.
The victory puts Liverpool atop the group, with nine points after three games, conceding no goals.
Manchester City coast to victory
Ferran Torres, Gabriel Jesus and Joao Cancelo were on target, as Manchester City made it three wins out of three in Group C, with a 3-0 win over Olympiakos at the Etihad Stadium.
The result leaves City three points clear of Porto at the top of the group and a single point in the return fixture on November 25 would secure progress to the knockout stage.
Torres put City ahead in the 12th minute, playing a smart one-two with Kevin De Bruyne, before confidently slotting home for his third goal in as many games in the competition.
Raheem Sterling had the ball in the net in the 32nd minute, but his effort was ruled out for offside, as City dominated play.
The Greek side grew into the game after the break and should have drawn level in the 55th minute, when a sloppy pass from Phil Foden fell to Mathieu Valbuena, but the 36-year-old French winger miscued his shot.
While Olympiakos rarely threatened, City needed another goal to ease their nerves and it came from substitute Gabriel Jesus in the 81st minute - the Brazilian hammered a shot in from close range at the near post after being slipped in by De Bruyne.
Defender Joao Cancelo made sure of the points in the 90th minute, leaving City in a commanding position atop the group, with a well-placed shot from outside of the area.
City now face Liverpool in the Premier League this weekend and Guardiola used all five subs in the second half, perhaps with half an eye on that clash with the league champions.
"In the first half, we played really well," says Guardiola. "In the second half, we struggled for some moments, but when we scored the second one it was over.
"We have five days to recover for Liverpool and then the international break. The forecast in the next three days says it will be sunny in Manchester.
"It's rare. We're going to recover and have a day off.
"After that, on Friday and Saturday, we'll prepare for the Liverpool game, but the players need a break."
Other results
Bayern Munich 6 RB Salzburg 2
Real Madrid 3 Inter Milan 2
Porto 3 Marsellie 0
Ajax 2 Midtjylland 1
Lokomtiv Moscow 1 Atletico Madrid 1
Mochengladbach 6 Shaktar Donestk 0
