Having suffered defeat in both test matches and all three one-day internationals the victory will be small consolation for the makeshift West Indies team which has been without its leading players throughout the games.
The tourists never truly recovered from a poor start which left them at 12 for three and they were not helped by four run outs.
Naeem Islam struck two fours and two sixes as he made 27 from 18 balls but then set off for an impossible run and wicketkeeper Devon Thomas threw down the stumps.
A total of 118 for nine was only going to be defendable if Bangladesh's spinners, who have tortured West Indies throughout the tour, found their groove quickly.
But West Indies had little trouble meeting the target with 19 balls to spare thanks to an aggressive 37 from Devon Smith and an unbeaten 37 from Travis Dowlin.
West Indies' leading players boycotted the test matches due to a dispute over contracts and payments and although they ended their protest the West Indies Cricket Board stuck with the back-up squad that had made themselves available.
