Batting first, Bangladesh set a target of 158 runs in their allocated 20 overs, losing two wickets.
Riding on 73 runs from Liton Das, the hosts set their final target after Najmul Hossain Shanto contributed 47 more.
Defending 158-2, Bangladesh made a brilliant start with the ball.
Taskin Ahmed grabbed two wickets while Tanvir Islam, Shakib Al Hasan and Mustafizur Rahman each took one wicket to steer their side to victory over the visitors.
Bangladesh's bowlers held their nerve defending the 159-run target, restricting England to 142-6 in their 20 overs.
Dawid Malan top-scored for England with 53 runs. (UNI)
