Australia won the toss and chose to bat first.
The Kangaroos scored 161/9 in their 20 overs with Shane Watson being the top scorer. The all-rounder made 60 runs from 39 balls with the help of four boundaries and four sixes.
Skipper Steve Smith made 36 runs from 29 balls with a boundary to his name while Aaron Finch contributed 33 runs from 24 balls after scoring six boundaries.
Dwayne Bravo grabbed four wickets while Sulieman Benn and Carlos Brathwaite grabbed three and two wickets respectively.
The Carribean side, chasing 162 runs to win, reached the target with three wickets and a ball to spare.
Skipper Darren Sammy made an unbeaten 50 from 28 balls after hitting six fours a maximum while Braithwaite scored 33 runs from 14 balls.
Andre Russell made 29 runs from 15 balls with the help of a boundary and three sixes while Johnson Charles scored 14 runs from 26 balls.
Josh Hazlewood dismissed three West Indies’ batsmen while Andrew Tye got two wickets.