Sulieman Benn took five wickets and Jerome Taylor reached the milestone of 100 Test wickets as Bangladesh crumbled to a 296-run defeat.
Shivnarine Chanderpaul remained unbeaten on 63 and guided his team to 4 for 208, an overall lead of 427.
Kemar Roach was at his devastating best as Bangladesh were reduced to 104 for 7 at stumps on day 2.
West Indies made a strong start to the second test against Bangladesh, their 500th test match, with a century stand from openers Kraigg Brathwaite and Leon Johnson setting them on the way to a first day total of 246 for 3.
Bangladesh have won the toss and have opted to field in West Indies 500th Test match at Beausejour Stadium, Gros Islet, St Lucia on Saturday.
The West Indies eye a clean sweep when they take on Bangladesh in the second and last Test starting at Gros Islet on Saturday.
Mushfiqur Rahim completed his third Test century but could not prevent West Indies from romping to a 10-wicket victory in the opening Test at Arnos Vale Sports Complex on Tuesday.
Bangladesh recovered to reach 256 for five on the fourth day of the first test in St Vincent after being asked to follow-on by West Indies.
Benn (5-39) was supported well by part-time offspinner Jermaine Blackwood, who claimed 2 for 14 as Bangladesh bowled out for 182.
Kraigg Brathwaite became the third-youngest West Indian to compile a Test double-century in leading the home side to a dominating 407 for three at the close of a rain-shortened second day of the first Test against Bangladesh at the Arnos Vale Stadium in St Vincent on Saturday.