Leg spinner Adil Rashid claimed a one-day international career-best four for 43 as England restricted Bangladesh to 277-6 in the series decider in Chittagong on Wednesday.
Rashid took full advantage of a turning wicket which remained under cover for two days due to rain and picked up his second four-wicket-haul in the final game of a three-match series which is currently tied 1-1.
The 28-year-old Yorkshireman derailed Bangladesh's innings with regular strikes in his unbroken 10 overs stretch after Tamim Iqbal and Imrul Kayes put on 80 runs in the opening stand.
Mushfiqur Rahim topscored for the home side with an unbeaten 67 while Sabbir Rahman (49), Kayes (46), Iqbal (45) and Mosaddek Hossain (38 not out) also contributed to what should be a competitive total.
Ben Stokes secured the first breakthrough for England when he had Kayes caught by substitute fielder Liam Dawson at square leg.
Local boy Iqbal became the first Bangladeshi to score 5,000 ODI runs by pulling Chris Woakes for a mid-wicket boundary.
But he fell the next over when Rashid deceived him with a googly and James Vince took the catch at short mid-wicket.
Mahmudullah, the top-scorer for Bangladesh with 75 in the Sunday's second match, hit Rashid for a six but then promptly fell to a short ball caught by Jonny Bairstow at cover.
Rahman fell one short of what would have been his fourth ODI fifty by edging Rashid to wicketkeeper Jos Buttler before Moeen Ali brought another lucky breakthrough for England by removing Shakib Al Hasan.
Hasan, who scored just four, missed the superbly turning delivery and so did Buttler but the ball deflected off his gloves to dislodge the bails with the batsman still out of his crease.
Rashid took his fourth wicket with a full-toss that Nasir Hossain tried to clear over the ropes only to be caught by Vince at mid-wicket.
Rahim and young Mosaddek put on 85 runs in their unbroken seventh-wicket partnership, taking Bangladesh past 250-run mark.
Rain had earlier threatened to ruin the match but it stopped just in time and the match started without delay.
England captain Buttler won the toss and opted to bowl first as the visitors looked to halt Bangladesh's unbeaten run in their last six consecutive series.