The hosts carried on from their overnight 95-2 to be bowled out for 265 after 112.5 overs.
Captain Kraigg Brathwaite carried on from his 42 on day one to eventually be dismissed for a marathon 94 off 268 balls including nine fours.
Vice-captain Jermaine Blackwood also showed good form with a 139-ball 63, also including nine boundaries.
Off-spinner Mehidy Hasan Miraz led the way with the ball, with 4-59 off 22.5 overs, while pacers Ebadot Hossain and Khaled Ahmed ended with figures of 2-65 off 28 overs and 2-59 off 22 overs, respectively.
Bangladesh then struggled to 50-2 off 20 overs, trailing the Windies by 112 runs at the close, with Mahmudul Hasan Joy (18) and Najmul Hossain Shanto (8) at the crease. Alzarri Joseph took both wickets for the West Indies.
The hosts won the toss and decided to bowl first, a decision which proved to be correct as the tourists were, at one point, struggling mightily at 45-6 after 15 overs of play with three top-order batsmen being removed without scoring.
They eventually recorded six ducks in total as a fighting 51 from captain Shakib Al Hasan and 29 from opener Tamim Iqbal helped the Bangladeshis stumble to 103 all out after just 32.5 overs.
Jayden Seales (3-33 from 10 overs), Alzarri Joseph (3-33 from 8.5 overs), Kemar Roach (2-21 from eight overs) and Kyle Mayers (2-10 from five overs) were the wicket-takers for the hosts.
In their reply, the Windies ended the day 95-2 off 48 overs, trailing Bangladesh by just eight runs. Captain Kraigg Brathwaite (42) and Nkrumah Bonner (12) are the batsmen at the crease while John Campbell (24) and Raymon Reifer (11) are the batsmen dismissed so far.
Pacers Mustafizur Rahman and Ebadot Hossain took the wickets.
Bangladesh started day four 132-6, trailing the Windies by 42 runs with Nurul Hasan on 16 and Mehidy Hasan yet to score.
After the entire morning session was delayed by rain and a wet outfield, proceedings got underway after lunch with the Windies quickly cleaning up the Bangladesh tail with the wickets of Mehidy Hasan (4), Ebadot Hossain (0), Shoriful Islam (0) and Khaled Ahmed (0).
Nurul Hasan was the only batsman to offer any resistance for Bangladesh with an aggressive 60 not out off 50 balls as the tourists were dismissed for 186 with Kemar Roach, Alzarri Joseph and Jayden Seales doing the damage with three wickets each.
Needing just 13 runs to win, West Indies openers Kraigg Brathwaite and John Campbell made short work of the total to secure the win and a 2-0 series triumph.
Final Scores: Bangladesh 234 and 186, West Indies 408 and 13-0.
