With test captain Pat Cummins competing in his first ODI in 22 months and Mitchell Starc restored to the team, Australia fielded a formidable attack after losing the opening two matches.
But it was Xavier Bartlett, who removed both openers and finished with 2-25 from five overs, and Adam Zampa, who took 2-34 from six, who effectively stifled home hopes of chasing down a challenging target at the JB Marks Oval after Australia were put in to bat and scored 322-9.
Rain brought a premature end to proceedings with South Africa on 145-4 after 28 overs, 46 runs short of their revised target of 191. Ryan Rickelton was unbeaten on 71 but running out of partners in a depleted batting line-up.
South Africa rested captain Temba Bavuma, David Miller and Marco Jansen and saw Tony de Zorzi hurt his hamstring while fielding, which meant he could not bat.
The wet weather also delayed the start of play, but Australia saw off any advantage South Africa hoped to gain out of the wicket with a 78-run partnership off 53 balls for the opening wicket between skipper Mitchell Marsh (56) and Travis Head (24).
The 20-year-old Oliver Peake contributed 48, while Alex Carey top-scored with 74 to push Australia to an imposing total.
South Africa won the first ODI in Durban by 67 runs and the second in Johannesburg by 32 runs. The two countries will now contest a three-test series starting in Durban next week.