West Indies failed to build a partnership as they lost all 10 of their second-innings wickets in the evening session on day three of the first Test as Australia dominated the hosts to win the match with two days to spare, at Kensington Oval in Barbados. West Indies needed 301 to win and they started promisingly as they overcame the early loss of Kraigg Brathwaite to reach 47-1 with John Campbell and Keacy Carty at the crease.
However, Hazlewood, who recently faced a lot of criticism for his performance in the World Test Championship (WTC) final shifted the momentum of the game as he ran through the West Indies top order during a characteristically controlled spell which saw four wickets fall for just nine runs.
West Indies were 56-5 and it was always going to be an uphill struggle for the hosts, even though Justin Greaves (38 not out) and Shamar Joseph (44) provided some late entertainment.
Hazlewood picked up Jomel Warrican's wicket to finish with 5-43 before Nathan Lyon bagged two wickets in the final over of the day, after play had been extended by 30 minutes, to seal the win.
Earlier, Australia had made a battling 310 in their second innings after Alex Carey had top-scored with a quick 65.
The visitors resumed the day on 92-4 but Travis Head and Beau Webster made gritty scores of 61 and 63 before Carey batted smartly with the lower order as Joseph took 5-87.
West Indies coach Daren Sammy met with match referee Javagal Srinath after play on day two to have a conversation about some of the decisions made by TV umpire Adrian Holdstock during the match.
Sammy said after the play on Thursday that he was unhappy with some of the dismissals, which were externally given by the South African using the technology. In the West Indies' second innings, though, Sammy could have few complaints.
The second Test match between West Indies and Australia will take place from July 2 to 7 at the National Cricket Stadium, St Georges, Grenada.
First Test, Bridgetown (day three of five)
Australia 180 (Head 59; Seales 5-60) & 310 (Carey 65; Joseph 5-87)
West Indies 190 (Hope 48; Starc 3-65) & 141 (Joseph 44; Hazlewood 5-43)
Australia won by 159 runs, lead series 1-0