Australia sent their hosts in to bat and South Africa amassed 365 for nine in their 50 overs, before bowling the visitors out for 333 in 49.5 overs as they continued their dominance over their rivals with a 19th ODI win in their last 25 meetings.
Australia were again undone by spin in the middle of the innings after a fast start to their reply and were not helped by the continued absence of seamer Pat Cummins and a side strain suffered by Nathan Ellis in the match that meant he bowled only four overs.
"It's really disappointing," Australia captain Mitch Marsh said. "We came here determined to level the series at 1-1 and take it into the final game but fair play to South Africa. I thought they played really well and outplayed us again.
"We just want to keep improving. We certainly don't want to be whitewashed, so we'll go to Potchefstroom determined to win that final game and play some good cricket."
South Africa made a cautious start to their innings and were rocked by the loss of Aiden Markram off the first ball, with Cooper Connolly taking a superb one-handed catch above his head off the bowling of Josh Hazlewood.
Bavuma scored his 103 from 116 balls for his sixth ODI century in a measured innings where he scored all around the wicket.
Miller was more explosive, with nine sixes in his 142 from 93 balls, clearing the ropes with ease as he struck his career-best score and eighth ODI ton.
There was little else of substance as the pair put on 156 for the fourth wicket and Jack Edwards, playing in his second ODI, was the pick of the bowlers with 5-67 in 10 overs.
In a carbon-copy of Thursday’s 67-run win for South Africa in Durban, Australia made a lightning start to their reply as Mitch Marsh (84 from 53 balls) and Travis Head (84 from 76 balls) put on 130 in 17 overs for the first wicket.
But the middle order struggled to score freely and South Africa’s three spinners tightened the screw.
Keshav Maharaj (2-54), Bjorn Fortuin (2-70) and Markram (1-55) were all effective in their 10 overs on a very good batting wicket.
Xavier Bartlett kept Australia in the game with a fine 50 runs from 28 deliveries but it was not enough.
"It was another really good all-round team performance," Bavuma said. "It started with the bat. Conditions were a little tricky up front but we managed to get through that period and build towards a good total.
"David played an unbelievable innings and then the bowlers did their job as well."
The final match is in Potchefstroom on Wednesday.