|Getaneh Kebede of Ethiopia|
The Walias lone goal came from second half substitute striker Getaneh Kebede who scored the late winner in the 88th minute.
Kebede had been on the pitch for less than 40 minutes after replacing midfielder Adane Girma at the start of the second half.
Ethiopia remains unbeaten in Group A on seven points from three games, two more than second placed South Africa.
Bafana meanwhile, collected their three points in the race to Brazil after beating third placed Central Africa Republic, who have three points, just 24 hours earlier in Cape Town.
Botswana stays bottom of Group A with one point from three matches ahead of their return leg fixture against Ethiopia on June 6 in Gaborone.