Liverpool had a winning start in Group D after a narrow 1-0 win over Ajax Amsterdam at Johan Cruijff Arena.
The Reds had three injury-forced changes among the four that included Virgil van Dijk, as Fabinho partnered the in-coming Joe Gomez in the heart of defence alongside recalls for James Milner, Georginio Wijnaldum and a rare start for Curtis Jones.
The sides were cagey in the early stages but the game was opening up just after the half-hour mark as Quincy Promes spurned a great chance for Ajax inside the six-yard box, with shot-stopper Adrian making a good save with his leg.
Jurgen Klopp's charges were fortunate to break the deadlock with ten minutes left of the first stanza after Nicolas Tagliafico turned a misdirected shot by Sadio Mane into his own net at the back post.
The hosts were unlucky not to head to the break level with Liverpool after Dusan Tadic latched onto a through ball by Daley Blind on the stroke of half-time and lobbed a shot over Adrian but Fabinho made a good recovery and cleared the ball off the line with an acrobatic kick.
Adrian was beaten again just two minutes from the break after Davy Klaassen was given space inside the box to hit a swerving shot towards the bottom corner but his effort came off the inside of the post and out of goal.
The Reds almost snatched the second goal in the last 13 minutes after a mistake at the back saw Diogo Jota chase a loose ball clear on goal but goalkeeper Andre Onana made a timely interception, as the visitors held to clinch all the three points.
Manchester City had a perfect start in Group C after thrashing FC Porto 3-1 at the Etihad Stadium.
Man City were without Kevin De Bruyne, Aymeric Laporte, Benjamin Mendy and Gabriel Jesus but they had a powerful attack led by Sergio Aguero, Raheem Sterling and Riyad Mahrez.
The visitors enjoyed a dream start as Luis Diaz fired them ahead in the 14th minute with a tight finish into the bottom corner after going on a long solo-run on the left wing before cutting inside to get the opener.
However, Porto's lead was short-lived as Aguero brought City level five minutes later with a strike from the penalty spot that goalkeeper Agustin Marchesin got a hand to but could not keep it out after Pepe collided with Sterling inside the box.
IIkay Gundogan gave Pep Guardiola's men a 2-1 lead in the 65th minute with a stunning free-kick from the edge of the box that dipped over the wall and beat goalkeeper Agustin Marchesin.
Ferran Torres put the game to bed for City in the last 17 minutes with a looping strike into the top corner after exchanging passes with Phil Foden on the left side of the box.
