The World Cup quarter-finalists emphasised their status as one of the pre-tournament favourites with a strong finish as they slowly overwhelmed their west African rivals in hot and humid conditions in Franceville.
Gyan, who caused a big stir when he left Premier League Sunderland in September in a loan move, repaid the faith placed in him by Ghana by scoring an excellent, long-range free-kick to open the scoring in the 63rd minute.
Injury concerns had made him doubtful before the tournament and again ahead of Saturday's match in the Gabonese provincial town, but coach Goran Stevanovic risked playing him.
Gyan's right-footed shot was driven wide of the diving Soumbeyla Diakite to keep up the high standard of goals at the tournament, being co-hosted by Equatorial Guinea and Gabon.
Ayew's effort in the 76th minute was as good as he cut in from the right wing, turned his defender one way and then the other before squeezing a shot inside the upright.
