The 28-year-old was named in coach Phillip Cocu's starting team and was impressive throughout the game but couldn't open his account or provide any assist.
The visitors took the lead by the 16th minute through Nigerian William Troost-Ekong but Giuliano Victor de Paula grabbed the leveller through penalty six minutes later.
Josef de Souza put Fenerbahce in front by the half hour mark which eventually sealed their victory.
Five minutes later, Ayew was cautioned after a rush tackle on an opponent, before missing the target narrowly with a shot outside the box. By the 62nd minute, he saw his close range shot blocked by Bursaspor's defence.
“Proud to play my first league game for FENER, 3 points. Gutted not to get a goal today inshallah soon... Our fans are incredible. Let’s prepare for Tuesday,” Ayew wrote on Twitter.
Proud to play my first league game for FENER 👊🏾 3 points 👍🏾gutted not to get a goal today inshallah soon... Our fans are incredible 💙💛 Let’s prepare for Tuesday 🙏🏽 @Fenerbahce pic.twitter.com/omC7DhMe9j— André Ayew (@AyewAndre) 11 août 2018