Zimbabwe knew a point from their home game against Kenya would be enough to secure a top-two spot in Group J, and saw out a 1-1 draw against the Harambee Stars to ensure they progress alongside Cameroon.
Elsewhere, Botswana missed the opportunity to book just their second appearance at the Nations Cup after drawing 1-1 at home against Mauritania in Group C.
Cape Verde were eliminated after a 1-1 stalemate at home against already-qualified Egypt, who did not call up Mohamed Salah and rested in-form forward Omar Marmoush.
Botswana now need a point from their trip to Egypt on Tuesday to qualify, while Mauritania will finish second in the group if they win at home against Cape Verde and the Zebras are beaten in Cairo.
Meanwhile, South Africa triumphed 2-0 in Uganda in Group K and Real Madrid forward Brahim Diaz scored twice as tournament hosts Morocco came from behind to win 5-1 against Gabon in Group B.
All four teams were already assured of progress before kick-off.
There are just two qualifying matches on Saturday, with both games in Group H.
Ethiopia have a home game against Tanzania (16:00 GMT) and Guinea welcome already-qualified DR Congo (19:00 GMT).
If Tanzania drop points then Guinea can qualify for the finals if they beat the Leopards.