This accomplishment marks Angola's successful progression beyond the group stage for the first time since 2010.
Both sides already knew they were heading through to the last 16 from Group D before kick-off in Yamoussoukro, but each could have gone through in first, second or third place depending on the outcome of this game.
Angola went ahead in the 36th minute when Ittihad of Alexandria striker Mabululu scored with a near-post header from Fredy Ribeiro's free-kick delivery for his second goal of the tournament so far.
Burkina Faso applied pressure in the second half as they went in search of a second goal, but Angola made sure of the victory in stoppage time at the end of the game.
A Jeremie Bela shot was not held by Burkina Faso goalkeeper Herve Koffi, and AEK Athens striker Zini pounced to convert the loose ball.
Having already drawn with 2019 champions Algeria and beaten Mauritania at the tournament in Ivory Coast, Angola top the group and will play a best third-placed team in Bouake in the last 16 on Saturday.
Ranked 117th in the world, this is just the third time they have made it out of their group, with the last coming when they hosted the tournament in 2010.
Meanwhile, Algeria's shock 1-0 defeat by Mauritania allowed Burkina Faso to finish second and so they will head to the northern city of Korhogo for a tie next Tuesday against the winners of Group E.
That will be Mali, South Africa or Namibia.
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