Earlier, last match’s centurion Iftikhar Ahmed carried on his belligerent form and hit 56 off 34 balls to help Barishal post 173-5.
Barishal skipper Shakib Al Hasan also chipped in with 30 off just 17 balls.
With the win, Barishal are equal with table-toppers Sylhet Strikers in terms of points as both teams have five wins in six games.
However, they are in second place behind Sylhet owing to an inferior net run rate.
Dhaka, on the other hand, are at the bottom of the seven-team table with just one win in six games.