Australia recovered from being 2-2 early in its innings to make 5-274 from the 50 overs largely thanks to a superb and unbeaten maiden international century from West Australian Voges.
The West Indies then lost Kieran Powell in the second over for two to start the run chase, but the tourists at no stage gave up the chase.
Charles and Darren Bravo got things well on track for the West Indies in a partnership of 106 before Bravo was out for 33 from 50 balls when caught by James Faulkner off the bowling of Xavier Doherty.
Dwayne Bravo then came and went quickly for 13 when bowled by Mitchell Johnson, but that brought Friday's centurion Kieron Pollard to the wicket to join Charles.
Charles did receive a life courtesy of the DRS when remarkably third umpire Nigel Llong gave him not out despite a clear sound and hot spot of an edge that went up onto his arm and up in the air.
Charles was 55 at that stage when it appeared Ben Cutting had him out, but the opener took full advantage of his second life hitting a two, six and four off the very next three balls.
He went on to record his first century as well in just his 10th one-day match for the West Indies with a previous highest score of just 45, but he was out straight after with a soft shot off Clint McKay. He made 100 from 121 deliveries with eight fours and a six.
Pollard was still at the crease, though, and appeared to be pacing his innings well with some help from Devon Thomas before the wicket-keeper batsman fell for 19 from 18 balls when unluckily run out.
Pollard was then caught in the deep for 45 off Faulkner to all but end the West Indies' run chase despite a late cameo of 23 from captain Darren Sammy.
Johnson finished with 3-50 for Australia with McKay taking 3-52 and Cutting, Faulkner and Doherty claiming a wicket apiece.
Earlier, Australia was in desperate trouble in its innings at 2-2 when Tino Best ripped through Shane Watson and Aaron Finch.
However, Phil Hughes (29) and Shaun Marsh (40) started the recovery mission for the Australians before Adam Voges and Brad Haddin kicked it into full gear.
Haddin made 43 from 45 balls and James Faulkner a not out 31 from 25, but it was Voges who was the star as he registered his maiden one-day international century and finish not out on 112 from 106 balls with 10 fours and two sixes.