Bangladesh lost the second Test of the two-match series by 17 runs as they were all-out for 213 runs in their second innings chasing 231 runs on the fourth day at the Sher-e-Bangla National Stadium, Dhaka on Sunday.
With the win, West Indies have clean-swept Bangladesh in the Tests, as they had earlier won the first Test in Chattogram.
Rahkeem Cornwall took four wickets in the second innings, total nine wickets in the match.
Mehidy Hasan tried his best to take Bangladesh to an impossible victory but finally his resistance came to an end as he edged one from Jomel Warrican to the first slip and Cornwall took a diving catch to end the match.
He made 31 runs and took Bangladesh close but finally could not take the team home.
Earlier, Bangladesh opener Tamim Iqbal scored a quick half century (50 from 44 balls) but departed shortly after reaching the landmark by chipping the ball to Shayane Mosely at short cover off the bowling of Kraigg Brathwaite.
Brathwaite also removed Soumya Sarkar (13) in a very unusual fashion as the opener edged the ball which bumped into the gloves of Joshua Da Silva but was finally caught by Rahkeem Cornwall.
Bangladesh lost seven wickes in the last two and half hours of Dhaka Test and suffered the second defeat of the series.
This is the first Test series win for West Indies in Asia since winning against the same opposition in 2012.
On the brink of Tea, Najmul maneuvered an over-pitched delivery from Cornwall and gave an easy catch to Moseley.
West Indies were all out for 117 runs in 52.5 overs in their second innings, setting up a target of 231 runs for Bangladesh to win.
Taijul Islam (4-36) and Nayeem Hasan (3-34) shared the final four wickets to dismiss West Indies within 23 minutes after the lunch break on day four.
West Indies lost three wickets early in the morning session of the fourth day but survived and stretched the lead to 211 runs, reaching 98-6 at the lunch break.
Nkrumah Bonner was the highest scorer for West Indies with 38 runs who survived more than three hours on the wicket.
Joshua Da Silva was the second highest scorer with 20 runs.
Bangladesh got some early success through pacer Abu Jayed, who dismissed night-watchman Jomel Warrican for his overnight two and then sent back Kayle Mayers out for six in a quick span of time.
Both the batsmen were judged leg-before before Taijul Islam dragged Jermaine Blackwood forward for stumping on nine.
But Bonner and Da Silva took their lead past the 209-run mark, the previous highest successful total in the fourth innings of a Test match in Mirpur.
After the interval, Bangladesh got quick success as Taijul removed Da Silva and Alzarri Joseph (nine) early after the re-start.
Bonner, who was playing for a long time tried to play a reverse sweep against Nayem Hasan, missed and the off-spinner hit the timber.
Mushfiqur Rahim took a fine catch on the deep mid-wicket region to dismiss Rahkeem Cornwall for one.
