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The Ghana international put the Eagles ahead with a brilliant goal in the 66th minute after striking the ball from the outside of the box.
Crystal Palace, however, could not hold on to the lead, with Amadou Onana drawing Everton level with just six minutes left on the clock.
Speaking in the aftermath of the game, which ended 1-1, Ayew paid tribute to former Crystal Palace boss Roy Hodgson, who stepped down last week after a poor run of results.
“When we speak about Roy, I have goosebumps because he's been so good to me & he's been a top manager, a top man,” the Ghanaian striker said.
“He helped me a lot, made me improve as a football player & as a man as well. I can't thank him enough.”
Ayew has now been involved in the second-most goals for the Eagles this season, having scored three goals and provided six assists in all competitions.
Last year, the 32-year-old signed a new contract at Crystal Palace that will see him stay at the club until the summer of 2025.
The former Aston Villa and Olympique Marseille forward has been with the Eagles since 2018 and has developed to become an important member of the team.
Hodgson’s departure may have come as a blow to Ayew, who was very much trusted by the English manager, but he could still play an important role under new manager Glasner after scoring in front of the former Eintracht Frankfurt boss.