By stumps on on Thursday’s opening day, Australia were 3-438 after winning the toss.
The woeful Windies’ worst fears were realised when veteran Voges (174no) and a re-born Marsh (139no) clicked in an unbeaten 317-run stand.
It is the second-highest fourth-wicket stand and fifth-biggest partnership overall in the 85-year Australia-Windies Test history.
Fears that the lowly Windies will be brushed aside within three days might only be scuppered by rain forecast on Friday.
Voges, 36, thrashed a run-a-ball 100 – the fastest Hobart Test ton – on his way to his highest score in a baggy green to snatch the match away from the hapless tourists.
He came out swinging after the pair came together at 3-121 just before lunch.
Voges was a calming influence on Marsh, giving selectors headaches with Usman Khawaja (hamstring) set to return for the Boxing Day Test.
Voges took up where Australian openers David Warner (64 off 61 balls) and Joe Burns (33) left off.
They crushed 15 boundaries as Australia cruised to 0-70 off the first 10 overs.
The Windies claimed the prized scalps of captain Steve Smith (10) and deputy Warner just ahead of the lunch break.
Left-arm spinner Jomel Warrican (2-111) had both Smith and Warner caught behind as Australia lost 2-17.
Enter Voges – he quickly struck his third Test ton, backing up last month’s 119 in Perth against New Zealand.
Voges made his first-class debut 13 years ago but did not earn a baggy green until June on this year’s tour of the Windies.
He averaged 71.25 this summer against New Zealand.
But the veteran was looking over his shoulder with the likes of Cameron Bancroft, 23, and Queensland teenager Matt Renshaw on the rise.
He will be breathing a little easier – as will Marsh, who had been expected to step aside for Khawaja in Melbourne before finally notching his first ton on home soil and third overall in his 17th Test.
The 32-year-old received a sixth coming as a Test batsman when he replaced Khawaja for the Adelaide day-night Test, striking a crucial 49 in the second dig.
On a horror day for the visitors, speedster Shannon Gabriel (ankle) was booked for scans late on Thursday.
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