Statistically speaking, Senegal dominated proceedings with over 60% possession and 16 goal attempts. However, with only three of those efforts finding the target, it's fair to say that the Lions failed to live up to expectations.
Zimbabwe held their own and looked to be heading for a goalless draw as the match entered the 90th minute.
Guatemalan referee Mario Escobar added six minutes of extra time and that allowed Senegal to eventually find the breakthrough.
Substitute Pape Gueye's effort had hit the arm of defender Kelvin Madzongwe and after a VAR check, Mane stepped up to take the penalty.
The Liverpool forward made no mistake from the spot as Senegal bagged all three points at the Kouekong Stadium in Bafoussam.
Mane's effort also made history as it was the latest winning goal in normal time at the Africa Cup of Nations since Bruno Zita Mbanangoye's effort for Gabon against Morocco in 2012.
Also in Group B, Issiaga Sylla fired Guinea to a 1-0 triumph over Malawi, with the two Group C encounters also finishing with the same scoreline.
Former Southampton midfielder Sofiane Boufal's 83rd-minute goal handed Morocco a 1-0 win over Ghana, while Aaron Boupendza's strike was enough to earn Gabon the points against tournament debutants Comoros.
Tuesday's action will begin with the defending champions Algeria as they take on Sierra Leone. A mouth-watering clash between Nigeria and Egypt is the second game of the day, while Sudan vs Guinea Bissau closes out the show.