Put into bat, Bangladesh rode on Mahmudullah's resilient century to post 275 for seven and then put up a spirited bowling show to pack England for 260 runs in 48.3 overs.
Man of the Match Mahmudullah (103) struck his first ODI ton to lift Bangladesh from 99 for four to a respectable score after stitching a crucial 141-run fifth-wicket partnership with Mushfiqur Rahim (89).
England medium pacers James Anderson and Chris Jordan bagged two wickets each.
Bangladesh bowlers, ably led by Robel Hossian (4-53), struck at crucial junctures to put England in trouble.
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Ian Bell tried to do the rescue act with a hard-working 63 but Hossian got the opener caught behind in the 27th over.
The middle-order wobbled only to be held by Jos Buttler (65), who fought hard but his seventh ODI fifty was not enough to save England's fading fortunes.
Hossian got good support from captain and pace spearhead Mashrafe Mortaza (2-48) and Taskin Ahmed (2-59).
Buttler and Woakes, with their seventh-wicket 75-run partnership, looked like taking the Three Lions to a win at one stage, but Bangladesh were just unstoppable on a day that belonged to them.