Ayew, who has bagged four times for Crystal Palace this season, played his second full match of the international break after helping Ghana defeat South Africa last Thursday.
Palace's 28-year-old forward netted cooly from the spot once Sao Tome and Principe's goalkeeper Eusebio brought down Emmanuel Boateng in the box.
James Kwasi Appiah's charges now sit top of Group C, their qualifying group for the Africa Cup of Nations 2021. In AFCON 2019 this summer, Ghana reached the Round of 16, with Ayew scoring two goals and a penalty.
Ayew has now scored 16 goals from 58 international appearances.
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