The Eagles came from behind to secure a 2-1 win from a match that was again dominated by VAR.
Jordan Ayew scored the crucial goal on 87th minutes after the video referee overturned the on-field linesman who originally flagged for offside.
Earlier Sebastien Haller had given West Ham the lead when he swept home before Patrick van Aanholt’s penalty levelled.
The Irons will look back with frustration after missing a number of good chances with the score at 0-0.
“It’s hard to accept. We were a bit unlucky with the decisions,” said Manuel Pellegrini.
“We scored a goal and took the lead but we had other chances, especially in the first half. I said before we started the season that the way we use VAR is the most important thing. We have nothing to complain about.
“Maybe a second goal would have decided the game. We had three good chances to score but didn’t manage to. I don’t think we played a bad game but we need to play better and keep improving. It was a good chance to be in the top three in the table.”