It was late drama as the teams shared the points in what was possible a fair result, though that may leave both coaches disappointed.
Zimbabwe took the lead through Panashe Mutimbanyoka when he headed home from a corner after nine minutes.
South Africa hit back in the opening seconds of the second half as Oswin Appollis provided a neat finish to draw them level.
They had a number of chances after that and were perhaps unlucky not to take the lead when Zimbabwe goalkeeper Raphel Pitisi appeared to carry the ball back over his line.
But minutes later it was Zimbabwe who took the lead, again from a corner, as home goalkeeper Bontle Molefe made a hash of trying to clear the ball and substitute Lexington Mujokoro bundled the ball into the net.
It looked as though that would be the winner, but a free-kick into the Zimbabwe box deep into injury-time was not cleared and Makola’s shot from eight yards was too strong for Pitisi.
Mozambique claimed a deserved 1-0 victory over Lesotho in their Group A opener, which was gifted to them by an early goal after nine minutes from Simon Cipriano.
It is the perfect start for the Young Mambas, who will be pleased as well with their clean-sheet against a combative Lesotho side.
Mozambique dominated much of the play and had the better chances in the game.
Group B gets under way on Friday when defending champions Zambia take on Namibia (kick-off 15h30), who return to the competition after an absence of some years, hoping to spring a surprise.
Zambia will be among the favourites for the title, but face a tricky start against a team that is always competition at all levels of COSAFA competitions.
Before that, the other game in the pool sees Malawi take on Comoros Islands (12h30) in another game that is tough to call.
Both sides will know that if they are to reach the semifinals, this is likely a must-win for them.
Only the top team in each pool as well as best-placed runner-up advance to the semifinals, while the two finalists at this year’s competition will win a place at the 2021 Africa Under-20 Cup of Nations.
You can follow all the action from Port Elizabeth live with our stream right here.