The tourists began the third day on 207-6, 376 runs behind the Baggy Greens' daunting first-innings total.
Hazlewood removed Jerome Taylor for a first-ball duck, but could not dismiss Jomel Worrican to take his hat-trick.
Australia captain Steve Smith enforced the follow-on due to his side's commanding position in the match, and James Pattinson rewarded his skipper by taking the scalp of Ravindra Chandrika in the second over of the innings.
Pattinson tore through the West Indies' batting order by removing Bravo, Marlon Samuels and Jermaine Blackwood to leave the tourists reeling at 24-4, while Mitchell Marsh then removed Denesh Ramdin for four.
Kraigg Brathwaite offered the only resistance as he powered his way to a half-century, but he was beginning to run out of batting partners as Pattinson claimed his fifth wicket by dismissing Jason Holder.
Brathwaite guided his side over the 100-run mark, but he was the last wicket to fall six runs short of his century when Hazlewood clinched the emphatic victory for the Aussies.