Chelsea striker Kalou put the Ivorians ahead in the 18th minute and his former team-mate made the points safe 11 minutes from time after the visitors had Aggrey Morris sent off in the 70th minute.
2012 CAF African Nations Cup winners Zambia, who beat Côte d'Ivoire on penalties to win the tournament in February, lost their opening Group D match 2-0 in Sudan. Goals from Mohammed Altahir (51) and Saif aldeen Mohammed (77) earned Sudan victory.
In Group B, Tunisia survived a scare before securing a 3-1 win over Equatorial Guinea. The minnows led 1-0 at the break thanks to Rouhen Epitie, but the hosts levelled in the 51st minute through Issam Jemaa.
Half-time substitute Hamdi Harbaoui made it 2-1 five minutes later and another replacement, Chadi Hammami, sealed the win two minutes from time.