The 2-1 goal was Faud Ibrahim's first international goal for Ethiopia. Making only his third appearance for the Walias Antelopes, the striker from United States second tier club Minnesota Stars struck after 13 minutes at the national stadium in Addis Ababa.
Ethiopia defeated fellow qualifiers Niger 1-0 in Addis Ababa and drew 1-1 with former champions Tunisia in Doha in other preparatory matches ahead of a return to the Cup of Nations after a 31-year absence.
The Antelopes - named after an endangered breed unique to the east African country that roams northern-region Mountains - face Burkina Faso, Nigeria and Zambia at the African tournament.
Defending champions Zambia and twice winners Nigeria are considered near certainties to fill the top two mini league places and qualify for the quarter-finals.