SA took the lead in the 26th minute when Keagan Dolly produced a beautiful cross for central midfielder Teboho Mokoena to blast past goalkeeper Petros Mhari.
The hosts continued to push for a second goal that would give them some breathing space, and nearly found it in the dying moments of the game when Bongokuhle Hlongwane struck a ferocious shot that Mhari palmed on to the crossbar.
The result, coupled with Ghana's draw against Ethiopia earlier, means SA (on 13 points) take a three-point lead and +5 goal difference to Ghana on Sunday.
Ghana (10 points and +3) can draw level with Bafana on a +4 difference with a 1-0 win. Then the decision on the group winner comes down to most goals scored, and the Black Stars (now level with SA on six) will be higher with another win, and progress to the final playoff round.
In this round, group winners will be paired against each other in a two-leg tie, with the winner securing a spot in next year's World Cup.
On social media, many kept the dream of qualifying alive. They praised Bafana Bafana and coach Hugo Broos for “making the country proud again”.