Malick Yalcouye opened the scoring in the 44th minute and Franck Kessie made sure of the three points with his 58th minute penalty.
This was the first round of matches in Group C of qualifying that also contains Somalia and the Gambia, who meet each other on Friday evening.
Speaking after the game, Ghana boss Carlos Queiroz hit out at the decision to award a penalty against his team.
He said on Yen: "That penalty, it's a joke. The penalty is a joke. I just saw it on the television.
"Because I need to be quiet and polite. It was 1-0 down, 1-0 down. I don't think that Ivory Coast needed the referee to come inside the game and create an unbalanced situation."
Cameroon, meanwhile, overcame Comoros 3-0 in their Group G opener.
David Nyengue (39') and Bryan Mbeumo (48') gave the Indomitable Lions a two-goal lead before Warmed Omari (51') reduced the deficit.
But Danny Namaso (81') made sure of the result at the Roumde Adjia Stadium with his late effort.
Cameroon boss David Pagou told his post match press conference: "It was laborious, it was the return to class for the national team.
"The organisations were a bit shaken, but we still managed to do the essentials. The essentials for us were to score goals.
"We scored, we saw a very beautiful team. So there you go, we will savor it and then between today and the next match, I think we have four days, so we will try to work and we will not want to mess everything up."
In other results, Namibia defeated Congo 1-0 (Bethuel Muzeu 47'), DR Congo overcame Equatorial Guinea 2-0, Mauritania saw off the Central African Republic 3-1 as Libya and Botswana played out a 2-2 draw in their Group H qualifier.
Tunisia were held to a 1-1 draw with Uganda as Zimbabwe beat Sierra Leone 3-2 in a thrilling encounter with Marshall Munetsi netting an 88th minute winner after they fought back from two-nil down.
Friday fixtures:
Sudan v Ethiopia
Tanzania v Guinea-Bissau
Mozambique v Senegal
Niger v Lesotho
Rwanda v Liberia
Malawai v South Sudan
Nigeria v Madagascar
Gambia v Somalia
Togo v Burundi
Mali v Cape Verde
Morocco v Gabon
Burkina Faso v Benin
Egypt v Angola
Algeria v Zambia
Saturday fixtures:
Kenya v Eritrea
South Africa v Guinea
