The Warriors defeated Eritrea 2-0, with Peter Ndlovu scoring both goals.
The forward opened the scoring after 11 minutes, by chipping the ball over the 'keeper and scored a penalty six minutes later after Zenzo Moyo was fouled in the box.
Zimbabwe and Mali are tied on 13 points but the Malian Eagles took the automatic qualifying spot on superior goal difference.
However, Zimbabwe could still qualify for their first ever finals as the best group runner-up, if Sierra Leone slip up against Gabon on Sunday.
Critically, goal difference might deny the Zimbabweans yet again should Sierra Leone win in Libreville.
The Leone Stars have ten points in Group Seven and a win would lift them to thirteen.
As both Sierra Leone and Zimbabwe have a goal difference of plus five, a victory of any margin will take the West African country's goal difference above plus five and heap more misery on Zimbabwe.
The Warriors have a long history of missing out on the Nations Cup at the very last minute, and are notoriously known as the 'nearly men' of African football.