Both Tests were won well inside four days.
A wet field washed out the first two sessions on Monday, but when Bangladesh resumed on 6-132, needing 42 more runs to make West Indies bat again, play lasted less than 12 overs.
Bangladesh's second innings extended nine more overs and 54 more runs before it was all over for 186. Nurul Hasan was stranded on 60 not out from 50 balls.
Needing 13 runs to win, West Indies openers John Campbell and captain Kraigg Brathwaite took 17 balls.
Bangladesh's 100th test loss came after it scored 234 and 186 and West Indies 408 and 13 not out.
When the day's play got underway, Mehidy Hasan Miraz got off with a mark with a boundary then was out next ball trying to block an Alzarri Joseph bouncer and edging behind.
Jayden Seales then bagged Ebadot Hossain and Shoriful Islam for ducks in the same over.
Seales, Joseph and Kemar Roach each took three wickets.
Khaled Ahmed was run out for a duck from the non-striker's end when Nurul wasn't looking for a run.
Nurul resumed from 16 overnight and blasted two sixes and five boundaries for his third Test fifty — all against West Indies — and four runs short of his career best.
The teams now play three Twenty20s and three one-day internationals starting Saturday.
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