Riyad Mahrez, who was inspirational in Leicester's Premier League title success last season, scored a late equaliser as Algeria earned a point in their first match of the tournament in Gabon.
The Foxes winger had put his side in front at Stade de Franceville, but goals from Kudakwashe Mahachi and Nyasha Mushekwi, with a penalty, saw Zimbabwe lead from the 29th minute until eight minutes from time when Mahrez found an equaliser.
Mahrez shot from 25 yards and Zimbabwe goalkeeper Tatenda Mukuruva should have done better as the clash finished all-square.
Algeria, the Desert Foxes, are seeking a first continental title since 1990, having failed to deliver two years ago when favourites.
And the team which can boast the talents of Mahrez and his Leicester team-mate Islam Slimani, Porto's Yacine Brahimi and Nabil Bentaleb, on loan at Schalke from Tottenham, were expected to sweep aside Zimbabwe.
All seemed to be going according to plan when Mahrez curled in left-footed from a tight angle.
Zimbabwe, featuring in the tournament for the first time in 11 years and after an absence of five editions, quickly responded and within five minutes they were level.
Mahachi struck from inside the box and then Zimbabwe went in front after Mokhtar Belkhiter was booked for felling Hardlife Zvirekwi in the box. Mushekwi converted from the spot.
Mahrez's equaliser was somewhat fortuitous. His shot from range went straight through Mukuruva.
Algeria had chances to win late on, with Leicester's Slimani among those who could not find the target.
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