Striker Ayew netted the only goal of the game on 71 minutes after tucking away Christian Benteke’s through ball.
The result leaves Palace nestled safely in mid-table, while the Seagulls sit four points above the bottom three, having drawn five and lost four of their past nine games in all competitions, since their victory over Bournemouth on 28 December.
The outcome in many ways mirrored Brighton's season so far.
The hosts dominated possession and carved out several opportunities to score but were eventually punished by their more incisive opponents.
Christian Benteke, a threat throughout for Roy Hodgson's side, created Ayew's winning goal against the run of play.
The Belgian forward turned away from a home defender to find his strike partner with a clever reverse pass, Ayew converting with a low shot under Brighton goalkeeper Mat Ryan.
The Ghanaian has scored seven goals in the league this season.