The tourists dismissed Australia for 225 but faced just one over in reply, scoring six without loss.
Play was held up for two hours, and when the conditions got better the West Indies were set a revised target of 151 from 24 overs.
However, when the players returned, only one delivery could be sent down -- a dot ball from Doug Bollinger --- before rain intervened again, forcing the match to be called off.
The six runs the tourists got were courtesy four byes and two wides from Bollinger.
After heavy defeats in the first two matches, the West Indies now need to win the remaining two to draw the series.
Michael Clarke [ Images ] top-scored for Australia with 46 before Ryan Harris swelled the team's total, hitting 21 from nine balls at the end.
Ravi Rampaul (4-61) and Dwayne Smith [ Images ] (3-45) were the pick of the West Indies bowlers.