Adil Rashid claimed career-best one-day international figures as Bangladesh gave England a target of 278 to clinch the series in Chittagong.
Rashid's 4-43 on a turning track owed much to taking advantage of several Bangladesh batsmen throwing their wicket away, with only Mushfiqur Rahim going past a half-century in the hosts' 6-277.
Mushfiqur, who finished with 67 off 62 balls, helped the Tigers flourish in the closing stage of their innings, which was uninterrupted as the anticipated rain failed to materialise.
The first half of this match, played in much fresher conditions to the humidity of the two ODIs played in Dhaka, passed without controversy as the teams moved on from the spats that overshadowed Sunday's game.
England captain Jos Buttler - who was given an official reprimand for his retaliation to being provoked by Bangladesh fielders on his dismissal, with opposite number Mashrafe Mortaza and Sabbir Rahman fined 20 per cent of their match fees - opted to field first on Wednesday.
Imrul Kayes, who overcame a nervy start to bring up Bangladesh's 50 with a huge heave for six over deep cover, was the aggressor in an opening stand of 80 before being dismissed by Ben Stokes for 46.
Tamim Iqbal became the first Bangladeshi to reach 5000 ODI runs, but failed to mark the occasion in style, falling for 45.
Rahman started like he had a point to prove after Sunday's events and raced to 49 before being caught behind off Rashid but, as teammates fell around him, Mushfiqur remained patient and initially accumulated steadily alongside Mosaddek Hossain (38 not out) before cutting loose in the final few overs having been given a life on 44 after being dropped by Stokes.
