West Indies captain Darren Sammy won the toss and sent Australia into bat with the tourists desperate to win and avoid a five-nil series whitewash.
Australia slumped to 2-2 early on with Tino Best on fire and then after a recovery partnership between Phil Hughes and Shaun Marsh, Voges and Brad Haddin steadied things further with a 111-run stand.
Voges went on with it from there to end up making 112 not out from 106 balls with 10 fours and two sixes as he became the 37th Australian to score a maiden one-day international century.
The 33-year-old is playing his 17th one-day match for Australia and after outstanding form of late for both Western Australia and the Perth Scorchers, his international career might finally be taking off after several false starts.
With help from 43 from Haddin, 40 from Marsh and an unbeaten 31 from James Faulkner, Australia posted 5-274 to now be in the box seat to secure a five-nil whitewash of the series against the West Indies.
Australia is without captain Michael Clarke with Shane Watson taking over the captaincy from him, but his innings was over before it got started with a fiery opening delivery from Best.
Watson tried to leave it, but the delivery grew on him and forced the opener to chop it back onto his stumps meaning he couldn’t back up his outstanding form of the last two matches since he returned to the Australian team.
In Best's second over he then tempted Aaron Finch into a pull shot and he only managed to hit it right down the throat of Sunil Narine at third man to leave Australia 2-2.
It continued to be hard going for the Australian batsmen with Sammy keeping it tight at one end and Best continuing his blistering spell at the other.
Hughes and Marsh fought through the tough period, though, to combine for a 62-run partnership before Hughes fell for 29 when caught by Kieron Pollard at point off Dwayne Bravo.
It was slow going for Hughes, though, with him taking up 61 balls but he did the job to steady things as did Marsh on his return to the one-day side after continued good form for both Western Australia and the Perth Scorchers.
Marsh made a solid 40 from 58 balls before being caught behind by Devon Thomas off Bravo with the score 4-82.
That brought Voges and Haddin together, and the pair took the initiative right off the West Indies taking the score to 5-193 when Haddin was out for a well-made 43 from 45 balls.
Voges from there really started to get going on his way to his century and Faulkner chipped in with a more than handy 31 from 25 balls.
Best started tremendously with the ball for the West Indies but finished with 2-71 from 10 overs. Bravo ended up 2-62 from eight with Kemar Roach taking 1-52 from 10. Narine was the best of them with 0-27 from his 10 with the Australian batsmen again unable to pick him.