Liverpool put its Europa League campaign back on track by beating big-spending Anzhi Makhachkala 1-0 on Thursday, and Inter Milan broke through Partizan Belgrade's resistance late on to win by the same score line.
Stewart Downing scored a rare goal at the start of the second half from outside the penalty area to clinch Liverpool's victory.
"It was brilliant goal," Liverpool manager Brendan Rodgers said. "He's had a rough ride here really. It's been a difficult time for him, but he got a great round of applause from the Kop and if you can get that from the Kop then it'll give you a massive lift going forward."
The five-time winners of the more illustrious European Cup had lost two of their three matches in the Europa League but are now top of Group A.
Liverpool has a two-point lead over Anzhi and Udinese, which lost 3-1 at bottom-place Young Boys.
In Milan, Inter took until the 88th minute to break the deadlock with Rodrigo Palacio's header winning the clash with Partizan Belgrade.
The victory kept Inter level with seven points with Rubin Kazan at the top of Group H.
Rubin beat Neftchi 1-0 courtesy of Alan Kasaev's first-half goal.
Atletico Madrid maintained the perfect start to its defence of its Europa League title, with goals from Diego Costa and Emre Belozoglu securing a 2-1 victory over Portuguese club Academica.
The Spanish club holds a three-point lead in Group B over Viktoria Plzen, which won 2-1 at Hapoel Tel Aviv.
Lyon emulated Atletico by making it three wins out of three in Group I, securing a 2-1 victory over last year's beaten finalists Athletic Bilbao courtesy of Jimmy Briand's late goal. Sparta Prague is three points behind after after beating Ironi Kiryat Shmona 3-1.
Unbeaten Newcastle is leading the way in Group D as the Ameobi brothers setup Gabriel Obertan's goal in a 1-0 victory over Club Brugge.
