Shane Watson smashed an unbeaten 41 from 24 deliveries to guide Australia to victory
A heavy downpour interrupted the Australians' charge towards their 192 target when they were 100 for one - 17 runs ahead of the Duckworth-Lewis par score after 9.1 overs.
All-rounder Shane Watson - man of the match in Australia's opening Group B triumph over Ireland on Wednesday - was once again in full flow, unbeaten on 41 from 24 deliveries alongside Michael Hussey, who made 28 off 19, when the heavens opened.
The Windies earlier posted 191 for eight from their 20 overs after captain Darren Sammy won the toss and stuck with his team's preferred tactics in this format, opting to bat first - their total underpinned by half-centuries from Chris Gayle and Marlon Samuels.
Opener Gayle smashed 54 off 33 balls - including five fours and four sixes - before a soft dismissal, caught and bowled by Watson, while Samuels plundered three fours and four sixes in reaching 50 off 32. He holed out to David Warner at long-on off the bowling of veteran spinner Brad Hogg.
Paceman Mitchell Starc and all-rounder Watson, who claimed 3-35 and 2-29 respectively, were the pick of the Australia bowlers, the former having been passed fit after recovering from gastroenteritis. Pat Cummins, Daniel Christian and Hogg also claimed a wicket apiece.
Australia suffered an early setback in their response when Warner - much to his displeasure - was given out caught behind by Denesh Ramdin off Fidel Edwards with the first ball of the third over, but not before the opener had racked up 28 from 14 balls.
However, they continued at a decent pace as Watson and Hussey set about reducing the 9.6 required run-rate which ultimately proved crucial.
The result left West Indies facing a winner-takes-all clash with Ireland on Monday to determine who will join Australia in the Super Eights.