The 28-year-old's goal saved the Yellow Canaries from home defeat as they came from behind to snatch a 1-1 draw at Sukru Saracoglu Stadium.
It was his second strike for his new side since a summer loan move from English outfit Swansea City.
Netherlands international Ryan Babel put the away side in front five minutes to half-time, thumping home a thunderous long-range strike.
Ayew, however, hit back for Fenerbahce in the 71st minute, beating his marker to head home Hasan Ali Kaldirim's cross.
Besiktas finished the game with 10 men when Caner Erkin was sent off for a second bookable offence but the 94th minute incident was little too late to be exploited by the hosts.
The Yellow Canaries sit 13th on the league table, nine places below Besiktas.
Ayew lasted for the entire duration of the game which tallied his sixth league appearance for his new club.
He would be hoping for his seventh when they play as guests to Rizespor in the Super Lig on Sunday