The hosts needed just over 1-3/4 hours on the third day at the Vivian Richards Cricket Ground to claim the remaining four wickets and send Bangladesh tumbling to 144 all out in their second innings.
Wicketkeeper Nurul Hasan resisted with a counter-attacking 64 but the writing was always on the wall for the Tigers after they resumed the morning on 62 for six – still requiring an improbable 301 runs to make the Windies bat again.
Shannon Gabriel added another wicket to his tally to finish with five for 77 while captain and fellow fast bowler Jason Holder picked up three for 30 and Miguel Cummins, two for 16.
West Indies wasted little time in getting the breakthrough when Holder removed Mahmudullah (15) with his first legal ball but second delivery of the day, squaring up the batsman and having him caught at third slip by Roston Chase.
Nurul counter-attacked, adding 25 for the eighth wicket with Kamrul Islam (7) and a further 55 for the ninth wicket with Rubel Hossain (16), to temporarily halt the Windies charge.
All told, the 24-year-old right-hander struck six fours and two sixes in a hasty 74-ball innings, recording the fastest half-century by a Bangladeshi on foreign soil.
Resuming on seven, he took a couple of boundaries off the second over from Gabriel before ripping into the same bowler a few overs later, with fours on either side of the wicket before clearing the ropes at long off in an over which leaked 17 runs.
Nurul raised his landmark off 36 deliveries in the next over from Holder, with a single to fine leg.
Along the way, he lost Kamrul, bowled middle stump by Gabriel before himself perishing at the hands of Cummins, caught and bowled trying to hit a short delivery back overhead.
With his dismissal went Bangladesh’s resistance and Cummins ended the innings two overs later when he rattled Rubel’s stumps.
Seamer Kemar Roach, who did not bowl in the second innings, was adjudged Man-of-the-Match for his five wickets for eight runs which sent Bangladesh crumbling to a record-low Test score of 43 in the first innings.
West Indies will go for a series win when the final Test bowls off at Sabina Park in Jamaica next Thursday.