After Darren Sammy dismissed the set batsman Naeem Islam, left-arm spinner Veerasammy Permaul earned his first Test wicket in the form of Bangladesh captain Mushfiqur Rahim.
Naeem Islam scored 17 boundaries on his way to the hundred and reached the milestone by guiding a Tino Best delivery down towards fine leg for a four.
West Indies' Ravi Rampaul, right, and Denesh Ramdin celebrate the dismissal of Bangladeshs Shakib Al Hasan.
Mushfiqur Rahim scored a handy 43 runs and had a good partnership with Naeem Islam.
Naeem Islam, playing only his 6th Test match, scored his maiden century in 228 balls as Bangladesh scored 455 runs with the loss of six wickets.