Opener Kieran Powell was batting on 41 and with him veteran Shivnarine Chanderpaul on nought at the interval.
Gayle greeted the debutant with aggression, smashing the first and fourth ball of the match by Gazi for big sixes before clobbering two fours off paceman Shahadat Hossain to threaten Bangladesh's bowling attack.
But the young spinner soon had revenge, having the flamboyant opener caught at long-off in his fifth over.
Bravo added 42 for the second wicket before miscuing a drive off Gazi and was caught at point to leave the West Indies at 74-2.
Marlon Samuels then helped add another 32 for the third wicket before falling to Hossain -- thanks to a good catch by Gazi -- in the last over before lunch after scoring 16.
Powell remained steady, hitting five boundaries and a six.
The tourists handed Test cap to 23-year-old left-arm spinner Veerasammy Permaul in anticipation of turn in the later stages of the match.