Abdennour Belhocini opened the scoring at the Mandela National Stadium after 29 minutes and Thabiso Kutumela levelled for South Africa with his goal on the stroke of half-time.
There was a nervous moment at the end of the game for Molefi Ntseki's makeshift side as Medhi Mergham went down in the box, but instead of being awarded a penalty, the Algeria attacker was booked for simulation.
Overall Bafana edged the possession with the Fenne Foxes not at their commanding best, following an impressive 3-0 defeat of Uganda in their CHAN opener.
But it was the North Africans who looked lively early on with Abderrahmane Meziane trying his luck after 11 minutes with a first-time volley that was dealt with by Bafana goalkeeper Samukelo Xulu, before a similar effort was blocked minutes later.
And it was ultimately Algeria who scored first as Belhocini reacted quickest to a loose ball in the area to volley past Xulu, just before the half hour mark.
Bafana showed some real determination to fight back and found a first-half equaliser through Kutumela, as he profited from deflected pass from Menzi Masuku following a superb through ball from Malibongwe Khoza.
Both sides created a number of half chances and with the game winding down, Bafana had the chance to steal all three points, but Algeria keeper Zakaria Bouhalfaya made a strong save to deny substitute Fortune Makaringe.
Mergham was then booked before Bafana celebrated a point, and will now look ahead to facing Guinea in their next game on Monday.