The 26-year-old, on as a second-half substitute, handed caretaker manager Leon Britton a relatively decent start to life at the South Wales outfit.
After a goalless first half, Luka Milivojevic opened the scoring for the Eagles from the penalty spot in the 59th minute.
Seven minutes later, Ayew who has featured in all of Swansea City’s league games this campaign was introduced for Luciano Narsingh and he turned out to be the saviour for the hosts with a sublime effort in the 77th minute.
The Black Stars forward could have doubled his tally moments later but his effort went wide.
Wilfried Zaha and Jeffrey Schlupp were on parade for the Eagles while Bakary Sako was introduced in the 76th minute for Yohan Cabaye.
Swansea, placed at the base of the Premier League log, are now four points adrift safety ahead of trips to Liverpool and Watford on Boxing Day and next Saturday respectively while Crystal Palace dropped to the 16th spot.