Set 267 to win after Bailey's unbeaten 125 rescued the Australian innings, the West Indies were cruising at 159 for three in the run chase, before the return of Starc to the attack turned the match again as the tourists were bowled out 212 in the 39th over.
Starc (5-32) had claimed the first three wickets in the West Indian innings, all lbw, to have them reeling at 33 for three, but when he came back into the attack the Australians were struggling, with opener Kieran Powell and Dwayne Bravo putting on a century partnership for the fourth wicket.
The left-armer took 5-20 as the Australians routed the West Indies for 70 in Friday's opening game en route to a nine-wicket victory.
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