Australia were 85 for three at stumps, 63 runs behind, with test debutant Adam Voges on 20 and Steve Smith, who batted for over two hours without hitting a boundary, on 17.
Voges, 35, survived when he offered a sharp chance which Jerome Taylor squandered at square leg.
Earlier, the West Indies won the toss and batted on a flat, dry-looking pitch, but their decision backfired as a decent start gave way to an ignominious collapse.
A combination of good bowling by the three-pronged Australian pace attack and injudicious shot-making led to the home team being dismissed inside 54 overs, losing their last nine wickets for 85 runs.
Josh Hazlewood with figures of three for 33 was the pick of the Australian pacemen, dismissing three top-order batsmen in 15 consistent overs during which he relentlessly attacked the off stump.
He also chipped in with an excellent catch just inside the fine leg boundary to send Marlon Samuels (7) back to the pavilion.
Left-armers Mitchell Johnson (3-34) and Mitchell Starc (2-48) bowled well and spinners Nathan Lyon and Steve Smith took one wicket each -- Smith with his second delivery.
Opener Shai Hope (36) top-scored for the home team and nobody else managed more than the 21 garnered by Jason Holder.
The West Indies have not beaten Australia in a test for 12 years or in a series since 1992-93, but they dismissed Warner cheaply, looping a catch to backward point off pace bowler Taylor.
Marsh needlessly played at a wide Holder delivery and sent an easy catch to first slip.
Clarke's dismissal was the most prized. After surviving a close lbw appeal against Bishoo, he was dispatched when the same bowler induced an edge to keeper Denesh Ramdin who notched his 200th test dismissal.
The match, being played at Windsor Park in Roseau, is the first of two tests.
It is Australia's first test since the death of Richie Benaud at the age of 84. Both teams are wearing black arm bands in honour of the former Australian captain and renowned cricket commentator.
(Reporting by Andrew Both in Cary, North Carolina; editing by Ed Osmond)
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