In the 252-run stand, du Plessis scored 125 runs while Miller contributed with 129 runs and it was an innings of remarkable hitting and great resilience, given where South Africa stood when the two took the pitch.
Australia will need 321 to win the series-defining third one-day worldwide against South Africa in Hobart.
South Africa are seeking their first ODI series win in Australia since 2009, while the home team are desperate to keep their momentum going ahead of the arrival of India for a three-format tour. Quinton de Kock (4) and Reeza Hendricks (8) were dismissed in the first 10 overs, to Starc and Stoinis, respectively.
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Aiden Markram with captain du Plessis by his side scored a decent 32 off 42 deliveries before falling to Starc in the 16th over. When Kagiso Rabada had Travis Head (6) caught by Markram at point, Australia were in big trouble at 39/3.
Australia, who bounced back from losing the series opener in Perth by six wickets to beat the Proteas by seven runs in Adelaide on Friday, won the toss and sent the tourists in to bat at Bellerive Oval. After a 107-run partnership, Stoinis got out for 63 runs without finishing the job for his team. "Then obviously it went upstairs". Our bowling is doing really well, but we're looking for guys to put their hands up to score big runs, because we're also finding ourselves three-down four-down when it comes to 20/30 overs and then you're under pressure, especially playing just seven batters.
With 87 runs needed off the last eight overs, the onus was on Glenn Maxwell to take Australia past the line and he began well by hitting Pretorius for four towards square leg to open his account. Full credit to South Africa.
"What I like about him is that he has different paces to his game", he said of Miller, who was also named man-of-the-series for his tally of 192 runs.
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Steyn was the pick of the bowlers for South Africa, returning 3/45 from 10 overs, while Pretorius got 2/61.
Earlier, South Africa were revived by centuries from du Plessis and Miller, who took them from a precarious position to well over 300.
Du Plessis and David Miller shared a 78-run stand before the skipper dragged Pat Cummins onto his stumps for 47.
Estimations of South Africa's tally were duly revised a few times, with the rate climbing from a humble 3.5 after 18 overs to well beyond the six mark.
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Du Plessis was dropped on 29 and Miller escaped an lbw dismissal on 41 that was overturned on review. But the nature in such chases, when you continuously need 10-11-plus an over, when you get a wicket then it becomes hard again.