Batting at No.4, Breetzke hammered 14 fours and two sixes on his way to 112 off 106 deliveries, before being run out by Cooper Connolly in the 47th over.
After being sent in to bat by Aussie captain Mitch Marsh in Durban on Thursday, the home side struggled to 5-168 before Breetzke joined forces with lanky allrounder Marco Jansen for a 107-run partnership.
Jansen was even more brutal than Breetzke, blasting seven fours and four huge sixes on his way to 75 off 59 deliveries.
The pair set South Africa on the way to an imposing total of 8-297, meaning the Australians would have to score at almost a run-a-ball to claim victory.
Hot off his heroics in Australia's clean sweep of the three-game series against Zimbabwe, Australian paceman Nathan Ellis again played a starring role, picking up 3-57 off his 10 overs, including a brilliant caught-and-bowled to dismiss David Miller for a painstaking nine off 25 balls.
Australia spinner Adam Zampa was expensive, but still picked up two wickets as his seven overs went for 50.
Paceman Josh Hazlewood made the initial breakthrough when he had opener Tony de Zorzi caught by Matt Renshaw for a seven-ball duck, leaving South Africa 1-6 after 3.1 overs.
Ellis then picked up the key wicket of South Africa's other opener, the destructive Quinton de Kock, caught by wicketkeeper Josh Inglis for 14 off 18 deliveries (one four, one six) to have the home side in early trouble at 2-29.
Earlier, NSW allrounder Jack Edwards was given his ODI debut for Australia after Marsh won the toss and chose to field.
Edwards, a 26-year-old seam bowling allrounder, has played one T20 for Australia against Pakistan earlier this year in Lahore.
Allrounder Cameron Green missed the series against Zimbabwe but was included in the playing XI after recovering from a shoulder injury, while pace star Mitchell Starc was also playing his first match of the tour.
Australia came into the series fresh off a 3-0 sweep of their ODI series in Zimbabwe, but haven't won a bilateral series against South Africa since 2014.
