Luke Shaw, in search of his first goal for United, came within inches of breaking the deadlock, but his fierce half-volley was tipped on to the post by a scrambling Adrian's boot as the sides went into the dressing rooms deadlocked.
However, they will both start against Watford at Old Trafford on Sunday, according to the United manager, with places still up for grabs ahead of the FA Cup final with Chelsea. We kept control of the game.
"We are the second best team in the Premier League, a fantastic competition with lots of good teams with six teams trying to finish first", said.
There was a more subdued atmosphere from the home fans at the end of another deeply frustrating campaign for the Hammers.
Marko Arnautovic again looks in the mood for the east Londoners.
Mourinho made wholesale changes following Friday's 1-0 defeat at Brighton, his side showing eight alterations as Marcus Rashford and Anthony Martial were two to drop out of the side.
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But Trump instead lobbed the "swamp person" charge at Donnelly, prompting the audience to break into a "Drain the swamp" chant. Donnelly has carefully nurtured a voting record that has, until now, avoided being considered by Republicans as too liberal.
"It's a big achievement for us", insisted West Ham manager David Moyes of keeping his side in the top flight.
With defences on top, Adrian made a string of saves to protect West Ham's clean sheet and justify his selection in goal ahead of England worldwide Joe Hart, who returned from illness but was only named on the bench. "This is a big club and there are big expectations from the supporters so they will need to improve".
Mark Arnautovic was the sole bright spot for David Moyes' team, regularly beating his man easily but found himself isolated too often and David de Gea wasn't truly tested over the course of 90 minutes.
Jesse Lingard was first to be denied with a fiercely struck long-range effort before Adrian showed quick reflexes to save from Alexis Sanchez and then get back on his feet to turn Shaw's effort onto the post.
Paul Pogba curled a couple of shots narrowly wide for Manchester United, and the France midfielder was booked in the dying stages for kicking out at West Ham's Mark Noble, who was also shown a yellow card as tempers frayed.