Australia’s innings was headlined by a welcome return to form for captain Aaron Finch, who scored 53 in an explosive 37-ball knock.
Finch and No. 3 batter Mitchell Marsh (75 off 44) combined for a crucial 114-run stand, Australia’s 10th largest partnership in T20 cricket.
It was Marsh’s third half-century of the series.
But Australia’s middle-order once again struggled against the West Indies spinner, with the visitors losing 4/20 in 23 balls following Finch’s dismissal.
Alex Carey was removed for golden duck after spooning a simple return catch to tweaker Hayden Walsh, while Moises Henriques and Ashton Turner both scored six.
The Aussies registered just 75 runs from the final nine overs, finishing on 6/189. Veteran all-rounder Dan Christian provided some late fireworks, smacking a quick-fire 22.
It was comfortably the touring team’s largest score of the series to date, but felt about 20 runs short of par considering their commanding position at the 10-over mark.
Walsh was the chief destroyer with the ball, finishing his four overs with figures of 3/27.
In response, the West Indies openers Evin Lewis and Lendl Simmons started the run chase by cracking 56 runs from the opening four overs.
But some economic bowling from Adam Zampa (2/20) and Marsh (3/24) restricted the hosts during the middle overs.
While wickets tumbled at the other end, Simmons (72 off 48 balls) kept the scoreboard ticking with regular boundaries.
But Marsh claimed two wickets in two balls in the 16th over to swing momentum firmly back in Australia’s favour.
The West Indies needed 36 runs from the final 12 balls for an unlikely victory, but Andre Russell and Fabian Allen collectively hit four sixes in Riley Meredith’s penultimate over to set up a thrilling finish.
“This is absolute carnage,” commentator Ian Bishop cried.
But the West Indies ultimately fell four runs short of the 190-run target, with Mitchell Starc showing his experience at the death.
Meredith finished with figures of 1/57 off four overs, the third most runs conceded by an Australian bowler in a T20 innings.
The West Indies hold an unassailable 3-1 lead in the five-match series – the fifth T20 commences on Saturday morning at 9.30am AEST.