The victory, achieved on the back of a century from Shane Watson and a superb spell of bowling from James Faulkner, means Australia lead the five-match series 3-0.
Faulkner (4-48) ripped apart the West Indies middle and lower order with an inspired display, capitalising on a resounding 122 from Watson earlier in the day, with the recalled opener gaining man-of-the-match honours after a scintillating knock.
Australia skipper Michael Clarke won the toss and elected to bat as the home side looked to wrap up the series. Watson was selected in place of Usman Khawaja, opening the batting with Aaron Finch, while the West Indies recalled Andre Russell to the team after his 54 in 24 balls at the same venue against the Prime Ministers XI a week ago.
Australia got off to a blistering start, racking up 89 for the first wicket with Watson bringing up a half-century in only 52 balls.
Aaron Finch made a rapid 38 off 41 before edging a slower ball from West Indies captain Darren Sammy to wicketkeeper Devon Thomas just when it appeared he was set for a big score.
At the other end, Watson looked in fine form and, in partnership with left-hander Phil Hughes, they slowly moved up the gears as Australia began accumulating runs at a rapid rate. Watson brought up his century off 102 balls before unleashing on the West Indian bowlers.
He moved swiftly to 122 before being caught by Kieron Pollard off a shorter delivery from Kemar Roach that he hooked towards deep-backward square leg.
Hughes again fell short of a century, caught behind by Thomas off the bowling of Sammy for 86, before Clarke fell for 15 when he was caught and bowled by Pollard.
Pollard also showcased his skills in the field and had the crowd on its feet as he claimed a sensational one-handed catch, leaping high to snag Glenn Maxwell.
The agile fieldsman was at it again later on, repeating the feat to end a delightful cameo from George Bailey who had raced to 44 off 22 balls, both wickets coming off the bowling of Sunil Narine.
Australia was far from downhearted, though, and ended their 50 overs with 7-329.
Chasing 330, the tourists made a solid start with Kieran Powell and Thomas, promoted up the order due to Chris Gayle being off the field for a number of overs late in the Australian innings with a side strain, getting off to a reasonable opening.
Thomas had moved onto 19 when he played a rash shot at a fuller length ball from Clint McKay as the first wicket fell for 54 in the ninth over.
Powell fell next, three short of a half-century, as he scooped a Maxwell delivery to a diving Matthew Wade behind the stumps.
That brought the Bravo half-brothers, Darren and Dwayne, to the crease together. The pair showed their understanding by sharing in a strong partnership with Darren reaching his 50 off only 67 balls and Dwayne following the lead in 44 deliveries.
The pair put on 114 and it took a superb quicker ball from Mitchell Starc that went straight through Dwayne Bravo, clean bowling him for 51, to end a promising innings.
At 3-195, the West Indies were still in touch with the required run rate but with their task was made even tougher as Gayle lasted only five deliveries before being bowled by Faulkner for two.
The Aussie paceman then sent Darren Bravo on his way three balls later with a similar delivery that swung away, ending his knock on 86. That left the West Indies reeling at 5-215 and requiring a sizeable innings from Pollard and Russell in order to save the series.
Clarke turned to Mitchell Johnson to make sure it didn't happen and the quick did just that - effecting a brilliant run-out of Pollard, who was slow out of the blocks at the non-strikers' end.
A slower ball then did in Ramnaresh Sarwan, shattering the top of his off stump for 12 as Australia took control.
Russell was the West Indies' best hopes of making the runs required but McKay gave Australia breathing space with the last ball of his spell, forcing a mistimed shot that went straight up to the air and was collected by Wade, ending an exhilarating knock of 43 off only 31 balls.
Sammy launched Johnson back over his head for a huge six but it mattered little as Faulkner cleaned up the remaining batsmen to finish with 4-48 off 8.3 overs as Australia sauntered home.