Michael Clarke playing a leg side shot during his knock of 37 runs off 65 balls in Australia's chase.
Kieron Pollard scored an unbeaten 109 runs and single handedly lead West Indies to a fighting total of 220.
Pollard, who hit a towering six to get to 99, completed his century with a single on next ball in the second-to-last over to complete his second ODI hundred against Australia.
Pollard hit 11 boundaries and two huge sixes in his 109 runs knock off 136 balls.
Ben Cutting (3 for 45) secured his first three-wicket haul in ODIs after being called into the team for the rested Mitchell Starc.
Australia pace bowler Mitchell Johnson (3 for 36) had the visitors in trouble at 17 for 3 after eight overs.
West Indian opener Johnson Charles of West Indies was bowled for a duck by Mitchell Johnson.
Opener Shane Watson scored 76 to back up his century on return from injury two days ago to lead Australia to a five-wicket win over West Indies in the fourth ODI.