Afghanistan batted first on a good pitch but squandered the opportunity as they were bowled out in a haze of loose strokes for 156 in 37.2 overs.
The Tigers were 27-2 in reply, but
a stand of 97 between Mehidy Hasan and Najmul Hossain Shanto helped them reach their target with 15.2 overs to spare.
Bangladesh next meet England at the same venue on Tuesday