Ayew's goal came on the end of a dancing run in which the forward tricked his way through the Hammers' defence before dinking the ball elegantly over goalkeeper Roberto.
Before the late winning strike, Cheikhou Kouyate netted his first goal for the club and Jairo Riedewald made an exceptional block to keep the visitors from stealing a victory.
The match saw Palace push with determination for firstly an equaliser after conceding to Robert Snodgrass and then to claim the winner in emphatic fashion.
It's worth watching for Ayew's goal alone, so head over to Palace TV by clicking here or 'Palace TV' in the official app to enjoy highlights of this Boxing Day clash now for free.