An overnight declaration on 179-3 set the tourists an unlikely 460 to win.
Wickets fell regularly but Denesh Ramdin (59) and Jason Holder (68), who came together at 150-5, hit half centuries in a 100-run partnership.
Mitchell Marsh, who finished with 4-61, dismissed both men as the Windies lost their last five wickets for 32 runs.
On a decent batting surface, all of the top five made reasonable starts to their respective innings.
Opener Kraigg Brathwaite knocked 31 off 34 deliveries before edging spinner Nathan Lyon to Steve Smith at slip, while Darren Bravo reached 21 before he pushed at a fine delivery from Peter Siddle and was caught by wicketkeeper Peter Nevill.
Rajendra Chandrika was trapped lbw by James Pattinson for a patient 37 off 130 balls and Marlon Samuels became the first of Marsh's victims, caught by Nevill for 19, to leave the tourists 118-4.
Jermaine Blackwood was the fifth to depart, adjudged lbw to Lyon for 20.
However, Ramdin and Holder dug in to take the Windies within 210 of Australia but when the former edged to Nevill, the Windies resistance ended.
Carlos Brathwaite lasted just four deliveries before being bowled by man-of-the-match Lyon, who claimed 3-85 for seven wickets in the match.
Holder's 86-ball knock, which included two sixes and seven boundaries, ended in tame fashion when he looped a simple catch to Josh Hazlewood at mid-off.
Kemar Roach then fended a short Pattinson delivery to David Warner in the slips before Pattinson raced in take a steepling catch at fine leg to dismiss a swinging Jerome Taylor and spark scenes of celebration.
The final Test is due to start in Sydney on Sunday.
Australia wrapped up a comfortable 177-run victory over West Indies on day four of the second Test in Melbourne to take an unassailable 2-0 series lead.