Voges grabbed his third hundred in 11 Tests with two runs off the penultimate ball of the session in Hobart to extend his fourth-wicket partnership with Marsh (42 not out) to 136 runs.
They came together shortly before lunch when opener David Warner's dismissal for 64 had reduced Australia to 121-3, pegging back the hosts after they had dominated the first hour.
West Indies opted for a four-pronged pace attack on a wicket with a greenish tinge but it was left-arm spinner Jomel Warrican who did the most damage, claiming the key wickets of Warner and skipper Steve Smith (10).
The tourists had rested their hopes of a Bellerive Oval upset on targeting Australia's middle order but thirtysomething Western Australians Voges and Marsh thwarted their ambitions.
Voges, who made his test debut against West Indies in Roseau earlier this year, got himself set before making a statement of intent by clubbing Warrican for four boundaries in one over.
The 36-year-old reached his half century off 55 balls and, with Marsh holding down the other end, kept up the scoring rate of more than five runs an over which Australia had maintained over the first two sessions.
It had looked like being a long, bleak day for the tourists when Smith won the toss and Australia's openers Warner and Joe Burns (33) racked up 70 runs in the opening 10 overs.
Warner reached half-century, his 11th 50-plus score in Tests this year, off 40 balls with 10 fours and looked to be cruising towards lunch when he nudged a Warrican delivery down the leg side into the gloves of West Indies wicketkeeper Denesh Ramdin.
Although Warrican was West Indies' most dangerous bowler, paceman Shannon Gabriel bowled the best delivery of the day, a 147.2 kilometres per hour fizzer which went through the gate and removed Burns's middle stump.
To add to West Indies' woes, skipper Jason Holder might find himself in trouble after only 50 overs were completed before the tea break. – Reuters
Original source: Voges comes good for Australia