Voges, who resumed on 9 after lunch and reached his century before tea at Bellerive Oval, was unbeaten on 174 at the end of play.
Fellow Western Australian player Marsh, made 97 in third session to finish the day on 139 not out as the frustrated West Indies bowlers failed to take a wicket after lunch.
Australia brought up its 400 in 78 overs, an average of over five runs per over, and finished the day with 4.92 runs per over.
Television commentator and former legspinning great Shane Warne was critical of West Indies captain Jason Holder for not taking the second new ball when it was available after 80 overs, and for not moving players in from the boundary to the slip cordon in an attempt to take a late wicket.
It was a big first day for scoring in the region, with New Zealand making 409-8 on the opening day of its home test against Sri Lanka at Dunedin.
Voges made his first-class debut 13 years ago but did not earn his first test cap for Australia until June on this year's tour of the Caribbean. It was the third career centuries for each player, and Marsh's first at an Australian ground.
Earlier, West Indies left-arm spinner Jomel Warrican took the important wickets of opener David Warner and captain Steven Smith as Australia went to lunch at 121-3 after winning the toss and electing to bat.
Warner and Joe Burns hit a combined 12 boundaries in an opening partnership of 75 runs from the first eight overs, but Australia went on to lose three wickets for 51.
Burns was clean-bowled by paceman Shannon Gabriel for 33 and Smith was caught at first slip off Warrican for 10. Warner scored 64 before being caught behind in the second-last over before lunch.
Gabriel left the pitch during the final session with a left ankle injury and was expected to undergo later scans. He finished the day with 1-59 off 10 overs.
The West Indies are coming off a 10-wicket loss to a Cricket Australia XI in a tour match last week
Australia gave fast bowler James Pattinson his first test start in 18 months, replacing the injured Mitchell Starc. Cricket Australia said Thursday that Starc, injured in the final New Zealand test last month, will undergo surgery on his right ankle.
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