Mashrafe Mortaza took four wickets to break the back of Windies' chase.
Tamim Iqbal scored an unbeaten 130 and shared a 207-run second-wicket stand with Shakib Al Hasan to guide Bangladesh to a tour-reviving 48-run win over the West Indies in the first limited-overs international.
After winning the toss and electing to bat and losing a wicket in the second over, Bangladesh recovered to post 279 for four set up by Iqbal's 10th ODI century and Al Hasan's 97 from 121 deliveries.
Mushfiqur Rahim's late cameo of 30 from 11 balls contained three boundaries and two sixes before he was dismissed on the next-to-last ball of the innings.
West Indies was in contention in reply until Chris Gayle was run out for 40 in the 22nd over and the hosts eventually reached 231-9 in 50 overs.
Mashrafe Mortaza led the Bangladesh bowling attack with 4-37 from his 10 overs and Mustafizur Rahman took 2-35.
West Indies dominated the two-test series at the start of the tour with commanding wins in Antigua and Jamaica.
The three-game ODI series will be followed by three Twenty20 Internationals.
