A Didier Drogba header in the last minute finished off the Black Stars after Gervinho put the Ivorians ahead in the first half and Siaka Tiene added another midway through the second.
The win put Ivory Coast, held 0-0 by Burkina Faso in their opening game, top of the group with four points from two matches. Burkina Faso are second with one point and Ghana, playing their first game in the three-team group, are third.
Ivory Coast defender Emmanuel Eboue was sent off in the 56th minute but Ghana failed to take advantage although they got a consolation goal with a stoppage-time penalty by substitute Asamoah Gyan.
Ghana must now beat Burkina Faso in Luanda on Tuesday to progress.
The group is a three-team affair after Togo withdrew from the competition following last week's deadly gun attack on the bus taking their delegation to the northern enclave of Cabinda.
After throwing away a hatful of chances against Burkina Faso, Vahid Halilhodzic's side proved far more efficient against Ghana at Cabinda's Chiazi National Stadium.
Chelsea midfielder Michael Essien, who only joined the Ghana team on Wednesday after bad weather delayed his departure from London, was left on the bench as four members of last October's under-20 World Cup-winning squad started the game.
Bakary Kone, who wasted several chances against Burkina Faso, was replaced on the right wing by Salomon Kalou in Ivory Coast's starting line-up.
DROGBA HEADER
In a clash pitting two teams who have qualified for this year's World Cup, the Elephants dominated the early stages.
Midfielder Didier Zokora shot from 30 metres but keeper Richard Kingson tipped the ball away.
In the 23rd minute Yaya Toure found Kalou with a defence-splitting pass down the right flank and the Chelsea forward fed Gervinho with the perfect cross for him to tap in.
Ghana went close to an equaliser when keeper Boubacar Barry was forced to stretch to deny Kwadwo Asamoah.
Coach Milovan Rajevac brought Essien on at half-time for Moussa Narry and striker Gyan replaced Dede Ayew.
Ghana's hopes were boosted when Eboue was shown a straight red card for a nasty tackle on Opoku Agyemang.
Mathew Amoah's volley then smashed the foot of Barry's post as the Black Stars piled on the pressure.
Tiene though made it 2-0 in the 67th minute with a stunning free kick that went straight into the top left corner.
Drogba put the result beyond doubt in the last minute when he headed home an Abdul Kader Keita cross.
Gyan converted a consolation penalty for Ghana three minutes into stoppage time.
