Mitchell Marsh struck 75 and then took three wickets to get Australia into a winning position but in the end it came down to paceman Mitchell Starc's stellar bowling in the final over to end the West Indies’ winning streak.
The West Indies won the first three games to clinch the five-match Twenty20 International series and went within one scoring shot Wednesday of making it four straight wins.
The hosts needed 11 runs off the last over but Starc bowled five consecutive dot balls before conceding a six on the final ball to secure a four-run win for Australia.
The Australians batted first and posted 189-6 in an innings twice interrupted by rain breaks, with Marsh belting his 75 from 44 balls for his third half-century of the series and sharing a 114-run second-wicket stand with skipper Aaron Finch, who contributed 53.
The West Indies started aggressively in reply, with openers Lendl Simmons and Evin Lewis racing to 62, taking 15 in the second over from Riley Meredith and 23 in the fourth over from Dan Christian.
Wrist spinner Adam Zampa was introduced early, in the fifth over, and had almost immediate success when he bowled Lewis for 31 from 14 deliveries.
Marsh's first wicket was a big one, having Chris Gayle (1) caught just inside the long-on boundary and the Australians rallied to peg back the run-rate.
When Marsh removed Nicholas Pooran (16) and Simmons, who blazed 72 off 48 balls, on consecutive balls in the 16th over, it appeared the West Indies counterattack had withered.
But there was sting in the tail.
Needing 36 off the last two overs to win, Andrew Russell and Fabian Allen took on the bowling and plundered Meredith for 25 in the penultimate over.
Russell struck a six on the first ball of the over and Allen (29) hit three consecutive sixes before edging the last ball behind, making the equation 11 runs required off six balls.
Enter left-armer Starc, one of the best fast bowlers in the world when he's on form.
Bowling from wide around the wicket and angling into Russell's pads, he reduced the scoring options to conceded just six.
Russell hit the last ball for six to finish not out on 24 to leave the home side at 185-6.
The fifth game is Friday.