Ayew found himself unmarked in the Everton box and composed himself well enough to slot the ball past goalkeeper Jordan Pickford.
Despite taking a commanding lead into the break, Frank Lampard’s side came back strongly in the second half to overturn the score.
Michael Keane kicked off the comeback by reducing the deficit in the 54th minute. Richarlison then restored parity with a quarter of an hour left.
Everton completed the turnaround in the 85th minute when Dominic Calvert-Lewin headed home the winner to preserve the Toffees’ Premier League status.
Meanwhile, Ayew’s goal was his third of the season, having struggled in front of goal for Crystal Palace this term.
The Ghana international made a slow start to the campaign and only netted his first goal before the 2021 Africa Cup of Nations (AFCON).
However, he has improved in recent weeks and was given a rare start against Lampard’s side during Thursday’s Premier League encounter.
Ayew will be hoping to keep his place in the team when the Eagles take on Manchester United on the final day of the season this weekend.