A seventh defeat in eight league games loomed for Sunderland when James Collins headed past Jordan Pickford immediately after the restart but there was some late joy for the hosts.
Former Liverpool player Fabio Borini had only just taken to the field to replace Billy Jones, who suffered a head injury, when he fired in a low shot past West Ham goalkeeper Darren Randolph.
West Ham, with 37 points, are virtually safe but Sunderland, with only two points from their last eight games, remain nine points short of safety with six games left.
Sunderland manager David Moyes said it had been a missed opportunity to close in on the teams above them.
"We need to win games and today we've got to take three points. It wasn't for the want of trying," he said.
"We'll keep believing we're in with a chance, somewhere along the line hope the football gods will shine on us."
West Ham manager Slaven Bilic said he had been disappointed with the concession of the late equaliser. "We have an unfinished job to do. We have to pick up more points to be safe," he added.
(Reporting by Martyn Herman; Editing by Toby Davis and Ian Chadband)
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