Australia relinquished the No.1 Test ranking earlier this year, now Steve Smith's side are at risk of surrendering their one-day crown.
Australia snapped a five-Test losing streak at Adelaide Oval on Sunday, recording a dead-rubber win over South Africa in the day-night clash.
The result eased the pressure and ensured the new-look national side didn't slip to fifth on the Test rankings.
Australia will be seeking to end a similar slump in the coloured clothing on Sunday, when they face New Zealand in the three-match ODI series opener at the SCG.
The visitors, minus rested pacemen Mitchell Starc and Josh Hazlewood, dropped all five games in last month's one-day series against South Africa, marking first time Australia had ever been whitewashed 5-0 in a bilateral ODI series.
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Those results have left Australia, who defeated the Blackcaps in last year's World Cup final, on the cusp of slipping as low as third on the one-day table.
The Proteas will claim the No.1 ODI ranking if Australia are beaten 3-0 in the upcoming trans-Tasman series, which features stops in Sydney, Canberra and Melbourne.
Smith's team would slip to equal second on the ODI table, alongside New Zealand, if they lose all three matches. The Black Caps host Bangladesh in an ODI series in late December, giving them an ideal platform to rise further up the rankings.
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The Chappell-Hadlee trophy will also be up for grabs during the next fortnight, having been reinstated last year.
NZ retained the trophy in Hamilton earlier this year, completing a 2-1 series win. Smith was booed by locals during the post-match ceremony, having objected to a controversial dismissal of Mitch Marsh.
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