A superb knock from Mushfiqur Rahim helped tigers to post a reasonable target of 238 losing eight wickets.
At 117-6 in the 32nd over, this score looked highly unlikely. But, the experienced Rahim stitched an 84-run partnership with Mehidy Hasan.
Both the batsmen batted sensibly before upping the ante in the death overs.
Rahim deserved a century, but strangely he decided to take a single off the penultimate ball. Nevertheless, he scored 98 crucial runs and has kept his team in the hunt.
After opting to bat first, Bangladesh lost their openers in the first powerplay. Akila Dananjaya, playing his first international match after four months, struck twice in three overs and reduced the visitors to 68-4.