Second game, first win: Jürgen Klopp has redeemed himself with Liverpool for the false start in the Champions League and scored the first points.
The "Reds" defeated Ajax Amsterdam 2-1 (1-1) thanks to a late goal by Joel Matip and managed their first success of the season.
Mo Salah gave Liverpool, who were at times oppressively superior, the lead (17th).
Mohammed Kudus (27th) equalized for the Dutch record champions before Matip made the late decision in the 89th minute.
At the start, the Klopp team suffered an unexpected 4-1 defeat at Italian Premier League club SSC Napoli.
Inter Milan could also celebrate.
The Italian cup winners won 2-0 (1-0) against outsiders Viktoria Pilsen in group C of the preliminary round and booked their first success a week after the opening defeat against Bayern Munich (0-2).
Former Bundesliga striker Edin Dzeko (20') and Dutchman Denzel Dumfries (70') scored for Inter, with German international Robin Gosens in the starting line-up.
Pilsen, who had to play outnumbered after a red card against Pavel Bucha (61st) in the last half hour, remain without a point.
Two goals in stoppage time
In Group D, Sporting Lisbon celebrated the next three thanks to a strong finish.
The Portuguese, who had clearly defeated Eintracht Frankfurt (3-0) at the start of the premier class, defeated Tottenham Hotspur 2-0 (0-0) thanks to late goals from Paulinho (90+1) and Arthur Gomes (90+3). ).
Tottenham, who scored 2-0 against Olympique Marseille in their opening game, are Eintracht's next opponents on October 4th.
In Leverkusen's Group B, FC Brugge achieved their next success.
A week after beating Bayer (1-0), the Belgian series champions were clearly superior in a 4-0 win at FC Porto.
Ferran Jutgla (15'), Kamal Sowah (47'), Andreas Skov Olsen (52') and Antonio Nusa (89') scored for Brugge.
Porto, who host Leverkusen in early October, are without a point after two games.