SA A seamers complete the job in Australia
Australia were 113/2 at the start of the final day, trailing by 180 runs thanks to early damage done by Simon Harmer the previous day.
He finished with figures of 3/106, while Kagiso Rabada and Marchant de Lange took two wickets each.
Tom Cooper converted his 42 not out overnight, to a well-played 82 off 144 balls before he was bowled by Rabada. The only other half-century was scored by Matthew Wade (60), who was eventually run out by De Lange.
The rest of the Australian batting order were unable to build partnerships as Peter Nevill (29), Michael Neser (23), Cameron Boyce (19) and Chadd Sayers (3) were dispatched by De Lange (2/54), Rabada (2/50), Hardus Viljoen (1/77) and Harmer.
Australia A captain Moises Henriques did not bat due to injury, leaving his side a batsman short.
The hosts were all out for 310, leaving South Africa an 18-run target for victory.
It did not come without its casualties, as Reeza Hendricks and David White lost their wickets to Marcus Stoinis (1/9) and Neser (1/9) for two and three respectively.
Rilee Rossouw scored the remaining 13 runs required for a well-deserved victory by the visitors.
The second Test will take place from 14-17 August at the same venue.
(File photo:Gallo Images)