It was Australia's second biggest victory in 114 tests against the Caribbean islanders and gave the hosts a 1-0 lead in a three-match series, which concludes with tests in Melbourne and Sydney.
Australia, who could return to the top of the test rankings with a 3-0 series sweep, made 583 for four declared in their first innings on the back of a world record fourth wicket stand of 449 between Adam Voges and Shaun Marsh.
Voges was named man of the match for his unbeaten 269 in the match-turning partnership with fellow Western Australian thirty something Marsh.
"It was a good win, the partnership between Voges and Shaun Marsh really set up the match for us and the bowlers did a terrific job again," skipper Steve Smith said in a pitchside interview.
"I thought Josh Hazlewood led the attack beautifully. It was nice to see James Pattinson back bowling the way he did and to get a five-for was an outstanding effort."
Darren Bravo scored a fine 108 in the first innings and Kraigg Brathwaite notched a defiant 94 in the second but questions will continue to be asked about the long-term future of West Indies test cricket after an otherwise hapless display.
"Tough three days for us, we didn't really start very well," captain Jason Holder said.
"We were pretty indisciplined in the first session of the test match and that carried on for the rest of the first day. That really set us back and then we were always catching up."
Hazlewood (4-45) took the lead as the hosts wrapped up West Indies' innings with only 16 runs added to their overnight tally of 207-6 on a chilly morning in Tasmania.
It was Pattinson, playing his first test in 18 months in place of the injured Mitchell Starc, who provided the spearhead after Smith had become the first Australia skipper in six years to enforce the follow-on on home soil.
Opener Rajendra Chandrika lasted just three balls before departing with his third duck in four test innings before Bravo (4) earned the questionable distinction of being dismissed twice in the same session.
Two overs later and Pattinson sent back Marlon Samuels (3) and Jermaine Blackwood (0) in successive balls, giving Australia a hat-trick chance for the second time in one day.
Pattinson was unable to convert and it was all-rounder Mitchell Marsh who next took advantage of the feeble batting, having Denesh Ramdin caught for four off his first delivery.
Holder put on 30 with Brathwaite before Pattinson returned to claim his fourth five-wicket haul in tests, the West Indies skipper flicking his 32nd delivery down the leg side and into the gloves of Peter Nevill for 17.
Nevill was again in action to dismiss Kemar Roach (3) off Hazlewood and the right-arm paceman got his sixth wicket of the match when Jerome Taylor holed out in the deep for 12.
Brathwaite was the final wicket to fall, bowled by Hazlewood (3-33), as West Indies pace bowler Shannon Gabriel did not bat in either innings after injuring his ankle on day one.
(Refiles fixing victory margin in headline and intro)
(Reporting by Nick Mulvenney, editing by Peter Rutherford/Amlan Chakraborty)
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