Manuel Lanzini put the visitors ahead after just three minutes and Noble added the second against the run of play in the 29th as West Ham earned its second win of the season — having beaten Arsenal away on the opening weekend.
Things got worse for Liverpool when Philippe Coutinho picked up his second yellow card in the 53rd minute as Brendan Rodgers' team fell to its first loss of the campaign.
Noble was then sent off for a lunging challenge in the 79th but Diafra Sakho polished off the win in injury time.
Related story
Liverpool fight back against West Ham to win five-goal thriller
