Brathwaite won the toss and decided to bat Thursday. The visitors were 1-84 with Shayne Moseley the other undefeated batsman on six.
Brathwaite and John Campbell (36), gave the side a decent start, making 66 for the opening stand. Campbell cut offspinner Mehidy Hasan past point for a boundary to begin his scoring on his 12th delivery.
Campbell also struck offspinner Nayeem Hasan for a six over long on as the Windies appeared to be in complete control.
But with the visitors scoring at apparent ease, Bangladesh got the vital breakthrough through left-arm spinner Taijul Islam when Campbell was trapped lbw trying to play a sweep shot.
Campbell reviewed the decision but it was in vain. His 68-ball innings included five fours and a six.