The tourists' tail resisted for two sessions on the third day led by Darren Bravo top-scoring with 81 and debutant all-rounder Carlos Brathwaite with 59.
But James Pattinson finally ended the West Indian resistance in the final over before tea, getting Bravo caught in the gully to finish with four for 72.
Off-spinner Nathan Lyon collected four for 66 and now has 179 career Test wickets.
Skipper Steve Smith did not enforce the follow on, preferring to give his bowlers a spell ahead of the back-to-back third Test, starting in Sydney on Sunday.
Bravo was in sight of his second century of the series after his 108 in the first innings in Hobart, before he sliced Pattinson to Smith in the gully to fall short.
Carlos Brathwaite's luck ran out when he spooned a high return catch back to Lyon to be out for 59 in the final over before lunch and end a dogged 90-run stand with Bravo.
Brathwaite was earlier given out twice only to be recalled both times for a front-foot no-ball by paceman Pattinson.
The Barbados all-rounder again was recalled on 50 when he hooked and was caught at fine leg only for replays to show another Pattinson no-ball.
Brathwaite clubbed his way to a 93-ball half-century with a massive straight six off Lyon and a single off the next ball.
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