Goals by Christopher Munthali and Given Singuluma gave the Chipolopolo (Copper Bullets) a two-goal half-time advantage. Ibrahim Salah halved the deficit from a stoppage-time penalty only for Mukuka Mulenga to score a third Zambian goal within a minute.
It was the first game in charge for Zambia coach Honour Janza, who took over last month when Frenchman Patrice Beaumelle joined compatriot and new Cote d'Ivoire boss Herve Renard. Sudan host South Africa on Friday in the opening matchday-one fixture and Zambia are at home to Mozambique the following day.
The 60,000-seat Chinese-built stadium replaces a much smaller national stadium that had become unsafe, and Zambia hope it will help secure the 2019 Cup of Nations. Zambia are competing with Algeria, Cameroon, Ivory Coast and Guinea to host the African football showpiece and the winners will be announced on September 20 in Addis Ababa.
Egypt are away to Senegal on Friday while Kenya are not involved having been eliminated by Lesotho in a preliminary qualifier.