In a contentious and sometimes controversial encounter that saw Sofiane Feghouli sent off early, half time sub Juan Mata slotted United ahead before Zlatan Ibrahimovic's late second sealed the deal.
The result moved United to within a point of Arsenal, who sit fourth - albeit having played a game more - and five behind second-placed Liverpool as we extended our unbeaten run of form to a thirteenth match unbeaten.
The game hinged on the controversial dismissal of midfielder Feghouli on the quarter hour mark.
Feghouli slid into a 50-50 challenge on the edge of the United box, and collided with the onrushing Phil Jones in an aggressive but legitimate coming-together.
Referee Mike Dean ruled that the foul was excessive force and sent the West Ham man from the field, leaving the match ten v eleven for 75 minutes.
To their credit, West Ham's dogged and spirited rearguard action restricted United until the 35th minute.
Darren Randolph saved superbly from Antonio Valencia after lovely link-up between Ibra and Henrikh Mkhitaryan, before Jesse Lingard somehow slammed the rebound off a post with the goal at his mercy.
David de Gea tipped a Manuel Lanzini effort wide and then beat away the Argentinian's effort from distance on the stroke of half-time.
Despite their numerical disadvantage, West Ham continued to threaten and De Gea again came to his side's rescue with a brilliant point-blank block to keep out Michail Antonio when one-on-one.
That proved crucial as, just three minutes later, the Hammers resistance was finally broken and United went ahead.
Substitute Marcus Rashford skipped past two defenders and cut the ball back for Mata who fired in an unerring finish from 18 yards.
Paul Pogba twice went close from distance but, with twelve minutes to play, United put the result beyond doubt through Ibra's 18th of the season.
Ander Herrera had a shot blocked and the loose ball dropped for our Swedish hero who beat the offside trap - and the advancing Randolph - to clip home.
That capped a patient and professional performance in our first London Stadium outfit to remain hot on the heels of the chasing Premier League pack.
Overall team performance: 6/10
United Faithful Man of the Match: Michael Carrick. Controlled the game and changed the tempo when he moved into midfield.