Egypt were without injured Mohamed Salah, Mohamed Elneny and Mahmoud Trezeguet, but were still expected to brush the Ethiopians aside in their Group D fixture played in neutral Lilongwe due to the latter's home venue not meeting Confederation of African Football standards.
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Goals from Dawa Hotessa and Shimelis Bekele sealed the Ethiopian victory, while Egypt, who were Cup of Nations finalists in Cameroon in February, managed just a single shot on target in an uncharacteristically limp display.
Morocco dominated their match against South Africa in Rabat, but fell behind to an early goal from striker Lyle Foster.
The pressure told for the visitors in the second period, though, as Youssef En Nesyri and Ayoub El Kaabi rescued the three points for the north African side.
Cameroon opened their qualification campaign with a narrow 1-0 away victory in Burundi as Karl Toko Ekambi scored the only goal of the game.
Mali scored twice in stoppage-time to beat South Sudan 3-1 in neutral Entebbe, with the Red Bull Salzburg duo of Mohamed Camara and Sekou Koita turning the match in their favour, before Aliou Dieng added a third.
Mali lost forward Ibrahima Kone to a red card with 12 minutes remaining but still managed to make it two wins from two.
Finally, Ivory Coast had 86% possession and 16 attempts on goal, but were held to a 0-0 draw by Lesotho in neutral Soweto.