United had the better of the first half, but they could not convert their chances and West Ham went ahead through Grady Diangana on 51 minutes.
Two minutes later the hosts' Luca Ercolani was sent off for a high challenge on Diangana.
Toni Martinez (pictured) doubled the lead with a header from Diangana's cross in the 69th minute, before Martin Samuelsen's powerful strike made it 3-0 two minutes later.
The result leaves West Ham in sixth, only behind fourth-placed Everton on goal difference. Man Utd drop into the relegation zone.
Man Utd: 15 Jan v Arsenal (A) PL2
West Ham: 12 Jan v Leicester (H) PL2