For the second successive game, Otto Addo’s side had to come from behind to win following last Thursday’s 1-2 triumph over Mali in Bamako.
Having opened the scoring after just six minutes via a penalty from Ayew, CAR ended the first half in the lead after Louis Mafouta netted a brace to overturn the result.
However, the Black Stars came back stronger in the second half, with two more goals from Ayew and another strike from Abdul Fatawu Issahaku propelling the hosts to a 4-3 win at the Baba Yara Sports Stadium despite Mafouta completing his hat-trick too.
Ghana coach Otto made three changes to the side that beat Mali last week, with Jordan Ayew, Abdul Fatawu Issahaku and Kamaldeen Sulemana coming on for Antoine Semenyo, Ernest Nuamah and Tariq Lamptey.
Addo also reverted to a back four, with Alidu Seidu, Gideon Mensah, Alexander Djiku and Mohammed Salisu protecting Lawrence Ati-Zigi in the post.
Thomas Partey once again partnered with Abdul Salis Samed in midfield, with Sulemana and Issahaku operating from the flanks.
Mohammed Kudus was also maintained from the team that beat Mali 2-1 four days ago in Bamako, while Ayew led the attack after coming off the bench to score against the Eagles.
The Baba Yara Stadium was sent into a frenzy just two minutes into the game when a surging run by Issahaku led to a penalty after he was brought down in the CAR box.
Ayew stepped up to calmly convert, making it his fifth goal in his last four matches for his country, as the Black Stars took the lead.
While Ghana looked to build on their early lead, their dominance was truncated by a goal against the run of play after Mafouta outran both Salisu and Djiku to net the equaliser in the 11th minute.
Six minutes later, a poor back pass by Djiku nearly resulted in another goal for CAR, but Ati Zigi reacted quickest to thwart Karl Namnganda’s effort.
Sulemana was also presented with a glorious opportunity following a blistering counter-attacking move but the Southampton winger made a poor decision by shooting off target despite having better options to his left and right.
With the first half heading for a stalemate, Mafouta stunned Ghana with his second of the night after taking advantage of Mensah’s decisiveness to score.
The second half of the game was, however, a different proposition, as Ghana upped the ante and began to use the flanks more, as Sulemana and Issahaku swapped positions.
After a series of near misses by Sulemana and Mensah, the latter delivered a pin-point cross which was met with a towering header by Ayew at the far post to make it 2-2.
Two minutes later, Issahaku put Ghana ahead after his deflected effort found its way to the back of the net before Ayew completed his hat-trick following a goalmouth scramble in the 69thminute.
There was, however, still time for some late drama, with Mafouta scoring his third goal of the night via a spectacular free-kick to make it 4-3.
Meanwhile, the Black Stars have now moved to the top of Group I in the CAF World Cup qualifiers, three points ahead of both Comoros and Madagascar, who will face Chad and Madagascar, respectively, on Tuesday.