The defending champion’s skipper Darren Sammy smashed James Faulkner for back-to-back sixes to claim victory with two balls remaining.
Australia had earlier set a target of 8-178 with Glenn Maxwell again the pick of the bunch with a hasty 45 from 22 balls, while Brad Hodge chipped in with 35.
But Chris Gayle’s quikfire 53 and Sammy’s late heroics with 34 from 13 balls did the job.
Yet again Australia were in a position to win, with the Windies needing 31 from the final two overs. But when Mitchell Starc was smashed for 19 from the penultimate over, the remaining runs seemed a formality.
Australia is now winless after two games following their loss to Pakistan in the opener.
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