Goals by Ryan Gravenberch and Diogo Jota earned Liverpool a 2-0 home victory over Belgian side Union Saint Gilloise on Thursday, giving them control of Europa League Group E with maximum points.
The hosts claimed a deserved lead a minute before halftime as Gravenberch calmly tapped in a rebound from close range after Union goalkeeper Anthony Moris had made an initial save.
Jota secured the win two minutes into stoppage time when he took advantage of a counter-attack and calmly rolled the ball past Moris from inside the box.
Liverpool top the group with six points and Union are third with one.
Toulouse are second in Group E with four points after a first-half goal by Gabriel Suazo gave them a 1-0 win against LASK.
Darwin Nunez thought he had given Liverpool an early lead by reacting swiftly to a rebound and calmly slotting the ball into the net, but the linesman had raised the flag for offside.
Liverpool manager Juergen Klopp admitted his team could have done better.
"We lost rhythm slightly and gave too many set-pieces away," he told TNT Sport.
"Should have had more direction and all these kinds of things, but you take what you can get in these moments and I thought we were really mature and professional but we could have been a lot better in a lot of moments."
Bayer Leverkusen secured a 2-1 victory at Norwegian champions Molde thanks to two goals in four minutes.
They top Group H with six points, alongside Azerbaijani side Qarabag who clinched a 1-0 victory at Hacken.
The 2022-23 Europa League runners-up AS Roma swept aside Swiss side Servette, Romelu Lukaku, Andrea Belotti and Lorenzo Pellegrini netting in a 4-0 home victory.
Villarreal secured their first points of the campaign with a 1-0 home win over Stade Rennais, the visitors wasting a great chance to equalise when Martin Terrier missed a penalty two minutes into stoppage time.