Jordan Ayew scored a penalty to put Ghana ahead, but Louis Mofouta's brace gave CAR a 2-1 lead at halftime.
However, Ghana rallied in the second half, with Ayew equalizing and Abdul Fatawu Issahaku's deflected shot putting them ahead.
Ayew completed his hat-trick in a scrappy finish, despite Mofouta's brilliant free-kick securing his own hat-trick.
With wins over Mali and CAR, Ghana now leads Group I with 9 points from four games.
The Black Stars will resume their qualifying campaign in October 2025 with a trip to CAR for their matchday five fixture.
