Mali qualified for the Africa Cup of Nations when drawing 2-2 with Group A rivals Liberia in Monrovia.
The Eagles finished on the same number of points as Cape Verde, but went through courtesy of a better head-to-head record against the island nation.
After Williams Dioh opened the scoring, Cheick Diabate replied before Cedric Kante gave Mali an 87th-minute lead.
But Patrick Wieh's injury-time equaliser failed to stop the Eagles reaching their third finals in a row.
Both Mali and Cape Verde boast 10 points from Group A, two more than Zimbabwe.
The Warriors will rue what might have been as an away win in Cape Verde would have taken them to the finals, but they lost 2-1 in Praia.
The islanders were 2-0 up after 13 minutes, thanks to goals from Valdo and Ryan, before Knowledge Musona reduced the deficit from the penalty spot after 68 minutes.
Zimbabwe only arrived in Praia on Wednesday, allowing just two full days of training ahead of the decisive clash.