The foundation of the successful chase was laid by a 120-run partnership by openers Hayley Matthews (66 off 45) and skipper Stafanie Taylor (59 off 57), who helped the team chase a stiff target of 149.
The moment the West Indies reached the target courtesy an overthrow, the entire dugout jumped in joy as the team joined the two not out batswomen, Britney Cooper and Deandra Dottin, in the middle.
What made the celebrations more special was the men's team, led by captain Darren Sammy, bowling coach Curtley Ambrose and all-rounder Andre Russell joined everyone in congratulating the girls.
The girls, as promised to Dwayne Bravo, danced to the beats of the all-rounder's latest rap compilation 'Champion'.
It was also the West Indies' first win over Australia in nine T20 Internationals.
Hayley was the star of their chase with a career-best innings, while Stafanie continued her sublime form with a solid knock.
After Hayley holed out at the midwicket in the 16th over, the West Indies needed 29 from 26 balls and the equation went down to 14 from the last 2 overs but the experienced Dottin made sure the team got home comfortably.
With three needed from the last over, Dottin took a single to give the strike to Cooper who ran a quick single and Aussies narrowly missed the stump as they complete the winning run from the overthrow.
Captain Meg Lanning (52) and opener Elyse Villani (52) scored brisk half-centuries before the West Indies fought back at the end to restrict three-time defending champions Australia to 148 for five.
Villani set up the tempo with her 37-ball innings and shared a 77-run partnership off 60 balls with Lanning, who continued her good run with second successive fifty.
The West Indies medium pacer Dottin bowled a superb last over with three dot balls and removed Ellyse Perry (28 off 23) and Erin Osborne (0) in successive deliveries to restrict the Southern Stars to an under 150 total.
Brief Scores
Australia women: 148 for 5 in 20 overs (Meg Lanning 52, Elyse Vilani 52; Deandra Dottin 2/33).
West Indies women: 149 for 2 in 19.3 overs.(Hayley Matthews 66, Staphnie Taylor 59; Kristen Beams 1/27).
West Indies women beat Australia women by 8 wickets.