Cameron Green's explosive 51 off 26 deliveries added firepower in a decisive 80-run partnership that rescued Australia from 78 for 4 in pursuit of 190.
West Indies looked poised for a massive total after fifties from Roston Chase (60 off 32) and Shai Hope (55 off 39) drove them to 123 for 1 in the 13th over. But Australia's bowlers, led by Ben Dwarshuis (4 for 36) and Nathan Ellis, applied the brakes, taking 4 for 7 in the final 16 balls to keep the hosts to 189 for 8.
Dwarshuis triggered the collapse with three wickets in the 19th over, while Ellis delivered pinpoint slower balls and yorkers to stifle the death overs. A stunning leaping catch by Green on the rope denied Hetmyer a six and capped a disciplined fielding display by Australia.
Australia's chase wobbled early with debutant Fraser-McGurk managing just 2, and key wickets of Marsh, Inglis, and Maxwell falling inside 10 overs. Green counterpunched, launching Alzarri Joseph for consecutive sixes to regain momentum.
Owen announced himself by pulling Andre Russell for six off his first ball and followed with a fearless attack against spin, launching Hosein for three sixes in an over. Green anchored the chase smartly, rotating strike before racing to his half-century with clean hitting against Holder and Motie.
Both set batters fell before the end, leaving Australia needing 15 off 21. Despite late nerves and a dropped catch in the deep, Cooper Connolly, Dwarshuis, and Sean Abbott held their nerve, sealing the win with seven balls to spare.