The Hammers took the lead on the stroke of halftime through a Michail Antonio penalty before a fine Mason Greenwood strike in the 51st minute brought Ole Gunnar Solskjaer’s side level.
The point was enough to secure top-flight survival for West Ham who moved up to 15th place on 38 points — four points above 18th-placed Watford.
United are in third place on 63 points, Chelsea are fourth, also on 63 points ahead of their game at champions Liverpool later on Wednesday. Leicester are fifth on 62 points.
(Reporting by Simon Evans Editing by Toby Davis)