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The 33-year-old middle order batsman blasted an unbeaten 112 off 106 balls to propel Australia to a commanding total of 274 for five, before the tourists' promising chase stumbled in the final overs with late wickets.
Johnson Charles, who replaced injured opener Chris Gayle, also scored a maiden ODI ton to give West Indies hope of hauling in the total, but the innings quickly petered out when allrounder James Faulkner had the hard-hitting Kieron Pollard caught for 45.
That left the Caribbeans at 234-7, still needing 41 with less than four overs to spare, and seamer Clint McKay wrapped up the match on the second last ball when tailender Tino Best slogged straight to a man at deep midwicket.
Australia completed the victory without injured captain Michael Clarke and several other first-choice players, who were rested to head over to India early to prepare for a four-test tour.
"They were cruising along pretty much without taking too many risks," stand-in captain Shane Watson said pitch-side in a television interview. "I think we held them out really well."
Watson scored a century and half-century to set up victory in the previous two matches, but was bowled for a duck with the first ball of the innings by paceman Best.
Best dismissed Watson's fellow opener Aaron Finch for one in his second over, but finished with an expensive 2-71.
Australia's top order crumbled to 82-4, but man-of-the-match Voges and Brad Haddin, recalled to the side in the absence of regular wicketkeeper Matt Wade, combined for a 111-run stand to steady the ship.
After Haddin's dismissal for 43, Faulkner added an unbeaten 31, teaming up with Voges to plunder another 81 runs in less than nine overs to set up the win.
After Kieran Powell was out for two in the second over, Charles and number three batsman Darren Bravo (33) added 106 runs before the latter was sharply caught at mid-off by Faulkner off the bowling of spinner Xavier Doherty.
After bringing up his 100th run, Charles pulled the next ball from McKay straight to Ben Cutting at short fine leg and trudged off the ground ruefully.
Pollard belted a six straight into the sight screen but came up short when he attempted another straight slog off the bowling of Faulkner and was caught by Finch at long on.
Paceman Mitchell Johnson (3-50) and McKay (3-52) combined to wrap up the tail as the hosts celebrated a dominant series sweep.