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.