Leicester City winger Abdul Fatawu Issahaku was fouled in the penalty box and the referee pointed to the spot for a penalty.
Jordan Ayew stepped up and made it count from the spot, sending Central Africa Republic goalkeeper, Dominique Youfeigane, the wrong way.
The visitors however responded six minutes later after forward Louis Mafouta picked a pass from captain Geoffrey Kondogbia before slotting home past Ghana goalkeeper Lawrence Ati Zigi.
The Amiens forward got his second of the night in the 41st minute to ensure Central African Republic goes to the break with the lead.
Back from recess, the Black Stars revamped their team with some fresh legs with the introduction of Antoine Semenyo, Elisha Owusu and Abdul Mumin.
Two more goals from Jordan Ayew in the 60th and 69th minutes ensured the Crystal Palace forward takes his tally for the Black Stars to 28goals in all competitions.
Leicester City youngster Fatawu Ishahaku also got his name on the scoresheet for Ghana in the 62nd minute.
Louis Mafouta sealed his Hattrick for the visitors with a 90th minute goal but wasn’t enough to earn a point for Raol Savoy’s side.
The victory leaves Ghana at the summit of the table with 9points in 4games and they take on CHAD in their next qualifying game.