Pollard hit 85 and Bravo scored 51 to share a 132-run partnership for the fourth wicket after the tourists lost three early wickets for 17 runs.
Pollard belted eight sixes and five boundaries in 74 balls before he was bowled by part-time spinner Mominul Haque.
Bravo faced 108 balls and hit three boundaries and a six.
Opener Chris Gayle's poor form continued, scoring 2 before being caught by Nasir Hossain off Shafiul Islam.
Devon Thomas added 2.
Islam, playing his first match in the series, claimed 3-31, Mominul Haque took 2-14 and Mahmudullah 2-38.
The series is level at 2-2.
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