Joel Matip proved the difference for Liverpool on a frustrating night for West Ham at the London Stadium.
Cody Gakpo and Lucas Paqueta opened the scoring for both sides in the opening 20 minutes to keep the score level for much of the match.
Both sides had ample chances in a helter-skelter tie but a strong showing from Liverpool saw the visitors leave with all three points.
More to follow.
WEST HAM - LIVERPOOL: MATCH FACTS
West Ham (4-2-3-1): Fabianski, Coufal, Zouma, Aguerd, Cresswell, Soucek, Rice, Bowen, Paqueta, Benrahma (Cornet), Antonio (Ings)
Subs not used: Areola, Ogbonna, Palmieri, Kehrer, Fornals, Downes, Lanzini
Goals: Paqueta (12')
Cards:
Manager: David Moyes
Liverpool (4-3-3): Alisson, Alexander-Arnold, Matip, Van Dijk, Robertson, Henderson (Thiago), Fabinho, Jones (Jones), Salah, Gakpo (Nunez), Jota (Diaz)
Subs not used: Kelleher, Gomez, Tsimikas, Carvalho, Elliott
Goals: Gakpo (18'), Matip (67')
Cards:
Manager: Jurgen Klopp
Referee: Chris Kavanagh