Orlando Pirates goalkeeper Richard Ofori started in goal as Christopher Nettey earned a debut for the Black Stars,
Ayew led from the front in the opening 20 minutes after breaking the deadlock with a powerful free-kick from point-blank range following a foul near the six-yard area.
Ghana quickly searched for a second towards the closing period of the first half, but John Boye failed to head home a free-kick from Ayew before Samuel Owusu battled to beat the opposite number.
Afriyie Acquah nearly carved out the host’s second goal in the last five minutes of the half with a teasing ball to Jordan Ayew, who dragged wide from a promising position.
Ghana had the ball in the back of the net for the second time in the match on the stroke of halftime when Ayew headed in a cross from Owusu, but it was disallowed following an infringement.
No changes happened following the start of the second half from either side, as the Black Stars looked to enhance their first half dominance.
The Black Stars went for a double substitution midway through the second half, with Nettey and Owusu recalled for Caleb Ekuban and Nicholas Opoku respectively.
Ghana made the game safe in the last ten minutes when Ayew drifted inside the area to unleash a belter, as the Black Stars cement top spot in Group C, six points ahead of Bafana who face Sao Tome and Principe on Friday.