Centre-back Siyabonga Sangweni volleyed in at the far post to score Bafana Bafana's first goal of the tournament.
The hosts, who drew 0-0 with Cape Verde in their opener, dominated against Angola yet lacked a cutting edge.
But South Africa got a second goal when Lehlohonolo Majoro slotted past the keeper from a tight angle.
Majoro started on the bench, one of five changes to the team line-up following South Africa's disappointing display on Saturday, and had been on the pitch for only two minutes when he scored