Following on 203 runs behind this afternoon, the tourists slumped to 123 all out and a 2-0 series loss with a sorry display.
Steven Finn was the pick of the England bowling, following up a five-wicket haul in the first Test at Lord's with five for 42.
Most of his good work came after James Anderson had set the tone by removing dangerous opener Tamim Iqbal, scorer of a scintillating century yesterday, second ball of the innings.
Anderson, making the most of seam-friendly conditions after a delayed start, went on to claim three for 16 in a superb opening spell.
Mahmudullah was the only Bangladesh batsman to offer any resistance, clubbing five fours in a briefly entertaining 38 but it could not mask the tourists' deficiencies.
Yorkshire's Ajmal Shahzad, 24, took four wickets in the match on his Test debut.