He lay on the turf while West Ham celebrated, unable to understand what had happened.
De Gea has had a mixed season — he leads the Golden Glove race for most clean sheets in the Premier League, but has made some costly mistakes.
United struck the post again in the 32nd minute, when the lively Antony's powerful drive was deflected into the woodwork and back.
Ten Haag's men, who have just 49 goals this season – the second lowest tally in the top nine – managed 11 shots in the first half but only one on target.
As the clock ticked down to half-time, De Gea denied Benarhama a second before a huge penalty appeal for a handball against Victor Lindelof, which was disallowed by referee Peter Banks.
West Ham again put the ball into the net at the start of the second half but was blown off by the referee for a foul on De Gea by Michael Antonio.
United were faltered badly and Tomas Soucek put the ball into the United net with less than 20 minutes left, but was again saved by the officials, ruling the goal out for offside.
Ten Haag broke down while throwing at Jadon Sancho and Marcel Sabitzer, before introducing Anthony Marshall for the ineffective Watt Weghorst, but he could not find a way back.
West Ham boss David Moyes praised the “huge character of his side”, saying that it would be tough for teams below them to catch them, even if they were not mathematically safe.
“The numbers haven't confirmed whether it puts you in the Premier League so we'll have to wait for the next game and try and get more points,” he said.
JW / DJ