Alexander Isak scored the first goal for Liverpool, while Cody Gakpo scored the final goal.
And with goals from strikers Isak and Gakpo, Liverpool secured their first victory after losses to Manchester City, Nottingham Forest and PSV Eindhoven.
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Letter to the Reader — Why We're Asking for Your Support ContributeLiverpool won 2-0 away at West Ham United on Sunday night, in the 13th round match.
Isak, who scored his first goal in the English top flight with Liverpool since his transfer from Newcastle United, scored in the 60th minute.
He was substituted eight minutes later.
The hosts were left without midfielder Lucas Paqueta, who received two yellow cards in the 83rd and 84th minutes, and was sent off.
The numerical advantage on the field was exploited by the guests led by coach Arne Slot. Gakpo scored in the second minute of extra time for 2:0.
Liverpool now has 21 points with the win and is in eighth place.
West Ham has 11 points in 17th place.