Rovman Powell hit two fours and six sixes in a 28-ball 61 not out as West Indies' 193/5 proved too much for Bangladesh to chase down in their second Twenty20 international.
Bangladesh scored 158/6 in reply as West Indies won by a comfortable 35 runs to take a 1-0 lead in the three-match series.
Opener Brandon King scored 57 runs in 43 deliveries and captain Nicholas Pooran hit a 30-ball 34 after West Indies chose to bat first on Sunday.
Left-arm pacer Shoriful Islam took 2-40 in four overs.
Bangladesh recovered from 23-3 as Shakib Al Hasan top-scored for the visitors with an undefeated 68 off 52 deliveries, including five fours and three sixes. It was the highest score of the match.
Pacer Romario Shepherd finished with 2-28 in four overs.
The first T20 on Saturday was a washout. Bangladesh reached 105-8 in 13 overs with the match already having been reduced to 14 overs per side. That game was the first cricket international at Windsor Park since it was rebuilt after being severely damaged in 2017 by a hurricane.
The third and last T20 is scheduled for Thursday in Providence, Guyana, followed by a three-match ODI series.
West Indies swept the two-match Test series against Bangladesh.
