The West Indies are the reigning Twenty20 World Champions so they had plenty of confidence coming into playing their favourite format of the game, and it showed out on the Gabba.
Captain Darren Sammy won the toss and elected to bat first and the West Indies did well to reach 6-191 from the 20 overs with Johnson Charles top-scoring with a terrific 57 from just 35 balls.
Australia was then virtually never on target in the run chase despite 51 from 33 deliveries from Adam Voges. Eventually, Australia ended up making 8-164 from 20 overs to fall 27 runs short of the West Indies' total.
The victory will at least give the West Indies a positive note to depart Australia on after losing the five-match one-day series 5-0.
Amazingly, not only is it the West Indies' only success of this tour of Australia, but it's their first win of any sort in the country since winning a Test match at the WACA Ground in Perth way back in 1997.
Chris Gayle returned to the West Indies line-up from a side strain, but his horror Australian summer continued when he made just eight when Nathan Coulter-Nile took a blinder of a catch on debut from the bowling of Josh Hazlewood.
The West Indies' innings then got on track, though, through Charles and Darren Bravo. Charles was coming off his maiden international century in the fifth ODI on Sunday.
He continued on his form in the only Twenty20 international to be played between the two teams and combined for an 88-run stand with Bravo. Eventually, Charles was out for 57 when bowled by Coulter-Nile.
Kieron Pollard then came to the wicket and Bravo fell shortly after for 32, but Pollard made 26 from 17 deliveries before being caught by Shaun Marsh off James Franklin.
Dwayne Bravo added 13, Andre Russell (23 not out), Sammy (20) and Narsingh Deonarine (6 not out) as the West Indies reached 6-191.
Faulkner was the best of Australia's bowlers finishing with 3-28 with Coulter-Nile taking 1-36 and Hazlewood 1-36.
It seemed like a huge run chase for Australia and the longer the home side's innings went, the more out of reach the target of 192 continued to look.
Aaron Finch made just four when he was bowled by Sammy before Marsh put on a solid stand of 74 with Voges before Marsh fell for 21 to a run out.
Voges then fell just three runs later with his 51 coming from 33 balls with fours and two sixes, and despite 9.5 overs still remaining, Australia still needed a further 110 runs to win and the chase never got going after that.
Brad Haddin did hit two sixes in his 22 and Coulter-Nile hit two sixes as well as he remained 16 not out at the end, but Australia never looked likely to get close to 192, and they didn’t finishing on 8-164.
Pollard took 3-30 from four overs with the ball for the West Indies with Sunil Narine claiming 2-19 and Sammy 1-30.