In reply, Australia lost in-form batter Will Malajczuk early. His opening partner Nitesh Samuel was dismissed for the first time in the tournament shortly afterwards, with Australia reeling at 45/2 in the 12th over.
Steven Hogan then briefly steadied the ship for Australia with Oliver Peake at the other end. But Jacob Basson picked up his second wicket to send Peake back in the pavilion for just 10 and keep South Africa interested.
Hogan continued to take Australia closer to the target with support from Alex Young. However, it was Basson again who broke the partnership and got rid of Hogan seven runs short of his half-century to bag his third wicket of the evening.
Jayden Draper and Young combined to eventually see through the chase and hand the defending champions their first win of the Super Six. Australia lead the Group 1 table with six points.