West Ham were denied a first Premier League win over Manchester United in seven years and 13 attempts by Daley Blind's stoppage-time strike.
The Hammers had looked like enhancing their European hopes and denting United's bid for Champions League football when makeshift defender Cheikhou Kouyate twice juggled the ball before, with his third touch, hitting a superb volley on the turn into the net.
Radamel Falcao missed a glorious opportunity to equalise 14 minutes from time, but Blind popped up to score late on and earn a 1-1 draw for the visitors, who finished the game with 10 men after Luke Shaw was sent off for two bookable offences.
Wayne Rooney, Falcao, Angel di Maria, Adnan Januzaj and Robin van Persie all started for Manchester United against an injury-depleted West Ham, who deployed midfielder Kouyate in central defence.
The fact goalkeeper David de Gea was the away team's best player after 30 minutes, saving twice from Enner Valencia, told how Louis van Gaal's expensively assembled side struggled to assert themselves.
Kouyate's deflected strike, after Rooney's poor header, sparked United into life, but they had not won away from home after conceding first since December 2013, and not at all under Louis van Gaal.
But they avoided following Liverpool and Manchester City in leaving Upton Park defeated this term as Blind swept the ball into the net when Carl Jenkinson, on his 23rd birthday, failed to clear Marcos Rojo's lofted ball into the box.
It was harsh on West Ham but extended Manchester United's unbeaten away run in the Premier League to seven games.
Juan Mata was the odd man out as Van Gaal made five changes, while Kouyate might have felt uncomfortable at the back on his return from the African Nations Cup and injury.
Alex Song's risky pass towards Kouyate almost gifted the visitors an opener inside five minutes. Van Persie intercepted, but was unable to control the ball.
The hosts then benefited from a poor defensive decision as Rojo failed to head clear Song's lofted pass and Enner Valencia struck a swerving effort from 25 yards which De Gea saved.
The goalkeeper denied the West Ham striker with a more acrobatic save from the resulting corner after James Tomkins had won the ball.
Even when United had a corner West Ham were a threat, as Adrian plucked Rooney's set-piece from the air before launching a counter-attack.
Diafra Sakho, in for the absent Andy Carroll, sitting the game out with an ankle problem, found Enner Valencia, who over-hit his return pass to enable United's Antonio Valencia to snuff out the danger.
Van Persie was perhaps fortunate to escape a booking for catching Tomkins with a flailing arm as the pair duelled for an aerial ball, but Tomkins recovered to head Aaron Cresswell's free-kick down into the six-yard box.
Fortunately for the visitors, De Gea who got to the ball first.
West Ham's pace troubled United again when Rojo miscontrolled a pass, lost out to Enner Valencia and clattered Mark Noble. Referee Mark Clattenburg played advantage, but Sakho's cross was poor.
A yellow card for Rojo followed after Di Maria had an effort from 25 yards saved by Adrian.
West Ham took the lead four minutes into the second period when United's defensive flaws were exposed.
Rooney failed to clear Noble's free-kick and the ball fell to Kouyate, who was being marked by the United captain.
The Senegal midfielder-turned-defender pulled the ball down with his back to goal, took a second touch to steady himself -- all the while with the ball in the air -- and struck a fierce finish through a crowded six-yard box, helped by a slight deflection.
The strike seemed to awaken United from their Sunday slumbers, with Falcao firing wide from 25 yards and Van Persie volleying at Adrian.
United's lacklustre afternoon continued when Falcao sliced horribly wide following a one-two with Van Persie, who had another effort saved by Adrian.
The hosts might have had a second, but De Gea saved from Noble and Kevin Nolan in quick succession and substitute Matt Jarvis could only head off target.
Marouane Fellaini, on for Januzaj, caused havoc and Blind's goal came when Rojo lofted the ball into the area and Jenkinson's weak header fell for the Dutchman to fire low into the corner.
There was still time for Shaw to be sent off for a second bookable offence after he caught Stewart Downing out wide as the Hammers were denied.