Patrick Kaddu's solitary goal was enough to book the Cranes, who needed to avoid defeat to go through, a ticket to Cameroon next year.
Having ended their 40 years wait by qualifying for the 2017 Afcon, Uganda have now qualified for back-to-back tournaments for the first time since 1974 and 1976.
The win should come as good news to their neighbours, Tanzania, who can also seal qualification by beating Lesotho on Sunday.
The Taifa Stars could claim Group L's second spot with a win in Lesotho on Sunday to qualify for their first Nations Cup in 38 years.
The group concludes in March with Tanzania hosting the Cranes while Lesotho will travel to Cape Verde.
Nigeria's drew 1-1 with South Africa in Johannesburg was enough to see them through, Mali beat Gabon in Libreville and Malawi's loss in Comoros sent Morocco through.