Marlon Samuels' first-ever hundred against Australia and a record-breaking partnership with Denesh Ramdin lifted the West Indies to a competitive 282 for eight batting first.
But half-centuries by captain Steven Smith and all-rounder Mitchell Marsh, together with a quickfire unbeaten 46 from Glenn Maxwell ensured that the target was reached with eight balls to spare.
However, when Smith was run out for 78 in the 42nd over, any hopes the West Indies had of claiming the victory that would have eliminated Australia were extinguished by Maxwell.
Displaying his full range of unorthodox shots, he crashed five fours and two sixes off just 26 balls to banish any lingering anxiety among his teammates in the dressing room. Marsh was left unbeaten on 79, his mature knock going a long way towards fulfilling a lot of the promise that has been expected of him in Australia's middle-order.
More From This Section
It was so different at the halfway point of the match following Samuels' superb knock, an effort that earned him the "Man of the Match" award.
Amazingly, they were his first two scores over 50 in ODI
cricket against the Australians for more than 14 years.
Ramdin, who matched his senior partner shot-for-shot in an entertaining innings of 91, joined Samuels at the crease with the West Indies faltering at 31 for three in the ninth over after Smith had won the toss and chose to field.
During the course of his innings, Samuels went past the landmark of 5,000 ODI runs while Ramdin became the first West Indies wicketkeeper to reach the plateau of 2,000 runs in this format of the game before Mitchell Starc broke the partnership by bowling Ramdin.
Two of the three sixes in his 92-ball innings were consecutive straight hits off Starc, the left-arm fast bowler finishing with figures of three for 51. He should have also claimed the wicket of Samuels but wicketkeeper Matthew Wade failed to hold on the chance offered when the Jamaican batsman was on 65.
"We put in a good effort but being a bowler short for most of the innings cost us," said West Indies captain Jason Holder, who could only deliver two overs before leaving the field with a leg injury.
"We have to lift ourselves to face South Africa on Friday and I'm confident of us putting in a good effort.