Sulieman Benn (5-72) was the hero with the ball for the Windies as they completed their victory inside four days at the Beausejour Stadium in St Lucia.
Bangladesh were dismissed for just 192 in their second innings in a Test the hosts controlled from the outset.
Shivnarine Chanderpaul (unbeaten 84 and 101 not out) was named man of the match, while in-form opener Kraigg Brathwaite was the player of the series.
After deciding against enforcing the follow on a day earlier, the Windies batted on until Chanderpaul brought up his 30th Test century.
Jermaine Blackwood finished 66 not out as the pair put on an unbroken 169-run partnership for the fifth wicket with the hosts declaring at 269-4.
That left Bangladesh needing 489 for victory, a target they were never going to reel in.
Openers Tamim Iqbal (64) and Shamsur Rahman (39) made a bright start while Mominul Haque made 56 as Bangladesh reached 158-2.
But it all went wrong from then on as Benn and Jerome Taylor (3-39) did most of the damage.
Bangladesh lost 34-8 as the Windies cruised to a 2-0 series win.
Man-of-the-series Brathwaite scored 324 runs at an average of 108 in the two Tests, including a double century in Kingstown.