Newly-crowed African player of the year Mahrez gave Algeria an early lead in the Group B match but Kudakwashe Mahachi quickly equalised and a penalty before the half-hour mark scored by Nyasha Mushekwi had the Warriors in front.
In an action-filled encounter Zimbabwe -- whose build-up to the finals was overshadowed by a row over bonuses -- were just eight minutes away from claiming a famous victory before Mahrez struck again to secure a share of the spoils.