A late strike from 21-year-old forward Bongokuhle Hlongwane secured a vital win for the South Africans at the FNB Stadium.
Hugo Broos' men lead Group G after two games, leaving the manager impressed by the team's progress within four days.
"I am very proud and happy today from what I saw on the pitch of my team. We made big progress in one week from what I saw in Zimbabwe,” Broos told reporters after the match.
"What I saw today, I saw a team with confidence who played a very good game. There was determination, there was a will to win, there was discipline and that is what I like.
"We will see if we can go on like this and make progress like we did now in this week and we will see where we’ll end at the end of the qualifying race."
South Africa will next face Ethiopia in a doubleheader in October, with Ghana playing Zimbabwe. Read Full Story