Australia fast bowler Josh Hazlewood claimed the remaining two wickets to bundle out the West Indies for 220 and then the openers added 22 runs to extend the visitors' lead to 201 at lunch on day three of the second Test at Sabina Park.
Resuming at an overnight position of 143-8, West Indies successfully managed to avoid the follow-on as Jason Holder showed a strong resistance by adding 77 more runs to their innings.
Holder proved his efficiency as a batsman as he remained unbeaten on a brilliantly made 82, which included 12 fours and two sixes, before his side got all out.
Hazlewood, who had claimed three wickets on day two, added two more wickets in his kitty by removing Kemar Roach (7) and Jerome Taylor (0).
Openers Shaun Marsh (14) and David Warner (8) will resume their innings after the break.