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.
Ghana had gradually taken control of the game after Mali produced the best effort of the first half - a free-kick from youthful striker Cheick Tidiane Diabate that hit one post, ran across the goal-line, hit the opposite pole and bounced to safety.
Ghana played with a makeshift defence after the suspension of central defenders John Mensah and Isaac Vorsah but did not allow Mali any clear chance in open play.
Ghana are now on six points in the group but mathematically still not yet sure of a quarter-final place. They next meet Guinea on Tuesday. Guinea and Mali have three points and Botswana, whipped 6-1 by Guinea earlier on Saturday, none.
Gyan, a record signing for Sunderland, is now on loan to Al Ain in the United Arab Emirates.
