After drawing 0-0 with Zimbabwe away from home, South Africa needed a good result against the Black Stars at the FNB stadium on Monday.
They got just that as Bongokuhle Hlongwane found the net late in the game.
South Africa were the better side throughout and could have scored more if not for poor finishing on the day as CK Akonnor's side were toothless.
In Group G of the World Cup qualifiers, Bafana Bafana are top with four points whilst Ghana places second with three points.
The result leaves South Africa in an excellent position with hope of securing world cup qualification after losing out on the 2022 AFCON.