The Tigers won the final game by 19 runs according to the Duckworth-Lewis-Stern method after rain interrupted play in the 18th over.
The West Indies had needed 50 runs to win off 17 deliveries with three wickets in hand before the match was cancelled.
Bangladesh won the toss Bangladesh time and decided to bat first. A whirlwind 61 by Liton Das helped the Tigers to 184/5 in the 20 overs.
Mustafizur Rahman took three wickets for 31 runs, while Abu Hider, Rubel Hossain, Soumya Sarkar and Shakib Al Hasan picked up one wicket each.
Spinner Nazmul Islam suffered an injury to his left hand after it was inadvertently stepped on by non-striker Rovman Powell in the 5th over. He was taken to the hospital and ESPNcricinfo reported that he had four lacerations on his hand.
Liton Das was declared Man of the Match.