The visitors remained unbeaten in the series as Cermaon Green and Josh Inglis combined to get them over the line with just four balls remaining.
Batting first after losing the toss, the hosts posted a competitive 205/9. They were driven by Sherfane Rutherford's brisk 31 off 15 balls and supported by Romario Shepherd (28) and Rovman Powell (28).
However, their innings faltered early with Shai Hope (10) and Brandon King (21) falling to Xavier Bartlett's pace, while Adam Zampa's 3/54, including key wickets of Roston Chase and Powell, curtailed their momentum. Aaron Hardie (2/24) and Sean Abbott (2/61) also chipped in, with Australia's fielding, highlighted by two catches from Glenn Maxwell.
Australia's chase began disastrously with captain Mitchell Marsh dismissed for a duck in the first over by debutant Jediah Blades (3-29). But Maxwell and Inglis teed off shortly after, blasting 66 quickfire runs before Inglis fell for 51 off 30. Maxwell continued to punish the West Indies attack and eventually holed out to Jason Holder Off Akeal Hosein for 47 off 18.
Mitchell Owen and Cooper Connolly then fell cheaply, but Green's unbeaten 55 off 35, his third half-century of the series, anchored the chase. His composed knock, alongside Aron Hardie's 23 off 16, guided Australia to 206/7 in 19.2 overs, with Green's straight drive ending the match.
The teams remain in Basseterra for the fifth and final T20I on Tuesday.
British and Irish Lions full-back Hugo Keenan was on top of the world after scoring the series-winning try in the 79th minute against Australia on Saturday.
The British and Irish Lions claimed an unassailable 2-0 lead in the Test series against Australia following a dramatic 29-26 victory in front of close to 90 000 fans at the Melbourne Cricket Ground.
Australia stormed to a six-wicket victory over the West Indies to claim an unassailable 3–0 lead in their five-match T20I series, chasing down 215 with 23 balls to spare at Warner Park.
Pakistan have announced their white-ball squads for the upcoming tour of the West Indies, with fast bowler Shaheen Shah Afridi returning to both the T20I and ODI formats, while young batter Hasan Nawaz has earned a maiden call-up to the 50-over side.
