The tourists made 220 all out after winning the toss and electing to bat, with Mike Hussey top-scoring with 67 and George Bailey hitting a maiden half-century before being dismissed on 59.
West Indies' hopes of a win appeared on a knife-edge when Australia took the wicket of Sunil Narine to leave them on 204 for nine.
Darren Sammy hit a boundary to leave the hosts on 220, needing just one run from the last three balls to win the game, but a horrible mix-up led to Sammy being run out by Brett Lee.
The five-match series is still tied at one win apiece, with the final two ODIs to come in St Lucia on Friday and Sunday. (AFP)
