Zambia took the early lead in Group D at the African Nations Championship by beating Zimbabwe 1-0 on Tuesday.
Isaac Chansa scored the only goal in the 57th minute for Zambia.
Mali and Uganda shared the spoils in the group's other game, finishing in a 2-2 draw.
Uganda's Joseph Ochaya found the opener on 14 minutes but Sekou Koita answered 10 minutes later for Mali.
A Farouk Miya penalty shortly before half-time again put Uganda ahead, only for Mail to equalise through Hamidou Sinayoko on the hour mark.