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Roberto Firmino and Mohamed Salah both scored two goals apiece, as Liverpool demolished Maribor 7-0 at the Stadion Ljudski vrt.
Braces from the Brazilian and the Egyptian, as well as efforts from Philippe Coutinho, Alex Oxlade-Chamberlain and Trent Alexander-Arnold, helped the Reds to their biggest Champions League win in a decade.
This was Jurgen Klopp's side's first victory in the competition this season, with Liverpool now top of Group E at the midway stage.
Here's how the players on either team rated:
NK Maribor
Jasmin Handanovic - 4/10
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The cousin of Inter goalkeeper Samir Handanovic did not cover himself in glory on Tuesday. He could not have done much for some of Liverpool's goals, but should have done better for others.
Martin Milec - 4/10
Milec was strong in the tackle at times, but he struggled to know when to follow Philippe Coutinho infield and when to stay wide. He was also unable to contribute going forward.
Aleksandar Rajcevic - 3/10
Was given the runaround by Liverpool's fluid frontline all night. Although he did make a team-high four interceptions, Rajcvecic's defending was of the last-ditch variety.
Marko Suler - 6/10
Suler was probably Maribor's best player on a dismal night. The centre-back read the game well but did not have enough quality to halt Liverpool's rampant attack.
Mitja Viler - 3/10
One of Maribor's only real chances fell to Viler, whose shot was saved by Loris Karius. Defensively, though, he was undone by Salah's speed and direct running.
Marwan Kabha - 6/10
Kabha was more composed with the ball than most of his team-mates, making 42 passes at the base of a midfield trio. He spent most of his time defending, though, which is not usually his strength.
Blaz Vrhovec - 4/10
Vrhovec made a couple of good blocks but was still unable to stop Liverpool cutting through Maribor's midfield. He used the ball well at times, but struggled when pressed by the opposition.
Martin Kramaric - 5/10
A gifted youngster who Slovenia have high hopes for, Kramaric showed some flashes of quality on Tuesday, but was generally unable to exert his influence on proceedings. This experience may do him good in the long term, though.
Valon Ahmedi - 4/10
Selected as a No.10 and tasked with linking the play and supporting Marcos Tavares, Ahmedi spent most of the game chasing shadows. That, of course, is not entirely his fault, but Ahmedi was wasteful when he did gain possession.
Damjan Bohar - 3/10
Bohar was playing as a second left-back at times, but his reading of the game and anticipation of danger could have been better.
Marcos Tavares - 4/10
The striker was isolated for much of the match, but he perhaps could have done better with his movement and hold-up play. He had only one shot on goal, and that was blocked.
Substitutes:
Aleks Pihler - 6/10
The midfielder was tidy in possession and worked hard, but like the rest of his team-mates, the gap in quality was clear.
Dino Hotic - 5/10
Was introduced in the 57th minute but struggled to stem Liverpool's attacks. Did not have many opportunities to contribute at the other end of the field.
Jasmin Mesanovic - N/A
Was introduced too late to make an impact.
Liverpool
Loris Karius - 6/10
A slightly low rating perhaps, but Karius had so little to do that it is difficult to hand him a higher grade. He dealt with Maribor's only real chance comfortably and looked in control of his area.
Trent Alexander-Arnold - 8/10
The right-back shuttled up and down the flank all night, spending much of his time high up the pitch. Alexander-Arnold put in some dangerous crosses and scored late on.
Joel Matip - 7/10
Matip was untroubled in a defensive sense but kept his concentration well - a weakness which has at times been exposed. His passing was crisp, although the Cameroonian was rarely hurried.
Dejan Lovren - 7/10
Like Matip, Lovren retained his focus and did what was asked of him. He had more touches and made more passes than any other Liverpool player.
Alberto Moreno - 7/10
Usually, a major threat going forward, Moreno did not need a second invitation to push forward. He caused problems with his pace and recorded an assist for one of Salah's strikes.
Georginio Wijnaldum - 6/10
Wijnaldum was probably Liverpool's most disappointing performer; he did not play badly and should not be criticised, but he did not take the game by the scruff of the neck in the same way as some of his colleagues.
Emre Can - 8/10
Deployed as a holding midfielder in Jordan Henderson's absence, Can was excellent. His passing was probing and penetrative and he was in the right place to break up rare Maribor counter-attacks.
James Milner - 10/10
Milner was magnificent throughout Tuesday's clash. Handed a rare chance in the centre of midfield, the former Manchester City man did not disappointing - he used the ball well, directed the play and looked so comfortable against admittedly poor opponents.
Mohamed Salah - 9/10
Salah has been both productive and wasteful early on in his Liverpool career, but it is impossible to argue with the numbers he is putting up. Dynamic and direct, he can be lethal when cutting inside onto his left foot.
Roberto Firmino - 9/10
Firmino linked the play well and proved himself to be an unselfish forward, even on a night in which he scored twice. He can still be profligate at times, but his work outside the penalty area is invariably tremendous.
Philippe Coutinho - 10/10
A perfect performance from Coutinho, who was on another level as compared to his opponents. He scored one, set up two and wreaked havoc as part of the front three.
Substitutes:
Dominic Solanke - 7/10
Brought on with 14 minutes left to play, Solanke looked dangerous against a tired Maribor backline.
Daniel Sturridge - 7/10
Sturridge selflessly set up Oxlade-Chamberlain's goal, but he did not contribute much else during his time on the field.
Alex Oxlade-Chamberlain - 7/10
Opened his account for Liverpool with the sixth goal. The ex-Arsenal man worked hard but still has work to do to earn a spot in the starting XI.
