Mustafizur Rahman had earlier played a key role in keeping Australia to just 121 for 7.
On a tough pitch to bat on, the visitors slipped to a 23-run defeat chasing a modest 132 for victory.
WI flounder with the bat again; Ashton Agar was impressive on his return while Mitchell Starc claimed another three wickets
Australia slumped to 45 for 6 with Akeal Hosein taking three quick wickets.
The case was confirmed minutes before the opening delivery.
Australia to tour Bangladesh for five T20Is in August, 20-member squad announced.