Defending a modest 189 for nine on another pitch that challenged the patience and technique of all batsmen, the Proteas bowlers were resisted only by opener Aaron Finch's defiant 72 before he was ninth out as the World Cup-holders folded for 142 off 34.2 overs.
By virtue of their margin of victory, South Africa also earned a bonus point and leapt from last to first on net run-rate over Australia, leaving hosts West Indies third. Competition resumes in St Kitts on Saturday with South Africa and Australia renewing their rivalry at Warner Park.
Rabada disposed of Usman Khawaja in his opening spell and returned to account for wicketkeeper-batsman Matthew Wade and tailender Nathan Coulter-Nile in an excellent display of controlled fast bowling. His effort was supported by Wayne Parnell, who shared the new ball and got rid of the dangerous David Warner in his very first over.
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Spinners Imran Tahir and Aaron Phangiso then tightened the stranglehold with two wickets apiece, while Tabraiz Shamsi, the left-arm leggie, marked his debut with the wicket of Glenn Maxwell in his first over to ensure there was no escape for the Aussies.
Earlier, Australia's fast bowling pair of Coulter-Nile
and Josh Hazlewood proved most effective with two wickets each in restricting the Proteas after de Villiers surprisingly chose to bat first on winning the toss.
"We didn't adapt well enough with the bat today," was Smith's assessment of his team's reply. "We've got a couple of tough games ahead of us now and we have to improve on this effort."
He claimed the vital wickets of de Villiers and J.P. Duminy in consecutive overs to reduce the South Africans to 104 for five midway through the innings, effectively killing off any realistic chance they had of posting a formidable total.
Hazlewood was even more economical in conceding 20 runs off 10 metronomic overs. He earned an LBW verdict against Quinton de Kock to break the opening partnership with Hashim Amla and returned to get rid of Parnell.
Wickets continued to fall regularly thereafter and it was left to the lower-order players Phangiso and Rabada to assist Behardien in lifting the South Africans closer to the 200-run mark.