Chasing 192 for victory, Australia were 100 for one in 9.1 overs when the heavens opened up.
Opener Shane Watson was batting on 41 off 24 balls while Michael Hussey was unbeaten on 28 off 19.
David Warner, who scored 28 off balls, was the only batsman to fall, to pacer Fidel Edwards.
Australia, who were 17 runs ahead of the par score when rain interrupted, needed another 92 from 65 balls to win the contest.