Australia had to work hard to set a target of 115 for seven at the Premadasa Stadium, in a match eventually headlined by seamer Julie Hunter's five for 22 as the Windies' last six wickets fell for 11 runs.
Hunter finished the match with two in two balls, for her maiden five-wicket haul. Australia strike bowler Ellyse Perry (two for 19) had already clean-bowled main dangers Stafanie Taylor and then Deandra Dottin - and off-spinner Lisa Sthalekar got through her four overs for only six runs.
The Windies could not get competitive thereafter, despite a stand of 48 for the fifth wicket between opener Juliana Nero and Shanel Daley.
West Indies had made an immediate breakthrough of their own, after Australia chose to bat first, when opener Alyssa Healy was bowled by Daley with just the second ball of the match.
Australia could not dominate against fine spin bowling, teenager Shaqana Quintyne and Daley each taking two for 23.
But it transpired they had made enough, and will therefore take on England back at the same venue on Sunday.