Daley Blind rescued a point for Manchester United with a 93rd-minute equaliser after Cheikhou Kouyate’s sublime volley put West Ham ahead.
Kouyate juggled the ball twice, swivelled, and volleyed in, after Mark Noble’s free-kick dropped in his path.
United looked to be running out of time when Blind volleyed home from 16 yards after Angel Di Maria’s cross.
The visitors finished with 10 men, defender Luke Shaw sent off for a second yellow card.
West Ham, who remain eighth in the table, have not beaten United since 2007 and they will feel they allowed a great opportunity to end that run slip.
The Hammers were on top from the early stages – hustling in defence and attacking with pace.
In contrast, United lacked creativity and were too easily dispossessed at Upton Park before Blind’s dramatic late comeback stretched their unbeaten Premier League away record to seven games.
David De Gea rescued the visitors three times in the opening half an hour, twice keeping out Enner Valencia – one a 25-yard drive and the other an acrobatic close range volley – before James Tomkins was denied by the Spaniard’s right foot.
United omitted Juan Mata yet their midfield struggled to carve out chances.
A mistake by Alex Song almost let in Robin van Persie but Hammers keeper Adrian’s only serious save of the opening half was a tame effort by Angel Di Maria.
West Ham got the breakthrough their play deserved in the 49th minute, Kouyate showing great skill to volley home after United’s defence had failed to deal with Noble’s set-piece delivery.
Noble went close to doubling the Hammers’ lead before United came strong in the closing stages.
Falcao looked certain to equalise in the 77th minute after combining with van Persie, but the Colombia forward stabbed wide from close range.
Van Persie was then denied by Adrian’s right leg before the Hammers keeper scrambled across his line to keep out Marouane Fellaini in a frantic finish.
It looked to be enough for the hosts – but there was still time for Blind to volley home after West Ham had failed to clear a ball into the area.
A dramatic finish was concluded when United were reduced to 10 men following a second bookable offence for Shaw.
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