The Chipolopolo won the game thanks to a hat-trick by in-form striker Given Singuluma.
The southern Africans opened the scoring after 36 minutes when Ignatius Lwipa made light work of three defenders on the right before crossing for Singuluma to tap in.
Four minutes later, Singuluma sent George Chilfuya through and his strike from inside the area found the back of the net but Mauritian referee Seechurn Rajindraparsad ruled it offside.
Zambia doubled their lead in the 51st minute when Singuluma connected Chilfuya’s cross before completing his hat-trick with four minutes remaining.
The forward was pleased with his effort, insisting that he wants to use the tournament to land a club in Europe.
“God has answered my first prayer and that was for me and my country to do well in this tournament and we have started well,” Singuluma told BBC Sport.
“My second prayer is that the European scouts at this tournament spot me so that I can move to Europe to continue my career.”
In the other Group A game late on Sunday Senegal beat Tanzania 1-0.
Striker Baila Mamadou Traore got the only goal of the game in the first half through a header.
The Teranga Lions will face Zambia on Wednesday in a top-of-the-table clash while Ivory Coast play Tanzania.