Chasing a modest 226, the hosts were precariously placed at 169 for eight before Shafiul Islam (24 not out) combined with Mahmudullah (21 not out) to steer their side to a dramatic victory with six balls to spare at Zahur Ahmed Chowdhury Stadium.
It was England`s second upset defeat in the tournament as their experienced bowlers buckled under pressure in the thrilling final moments to make the task easier for the hosts.
England had suffered a humiliating three-wicket defeat at the hands of Ireland in an earlier league match.
Bangladesh had bowled out England for a modest 225 after electing to bowl as their bowlers, specially the spinners, did a fantastic job.
Bangladesh were staring at defeat as they were 169 for eight in the 40th over but Shafiul and Mahmudullah batted with grit under intense pressure with a match-winning 58-run unbeaten partnership for the ninth wicket.
With this win Bangladesh have moved to fifth place in the points table with four points and England are standing at third with five points.
England now must win their last encounter against the West Indies while Bangladesh have two more match to play against The Netherlands and South Africa.
Bangladesh almost messed up the run-chase by slumping to 169 to eight from a comfortable 155 for three, rasing hopes of England, but Shafiul and Mahmudullah ensured that the hard work done by their bowlers does not go waste.
Ajmal Shahjad (3/43) and Graeme Swann (2/42) did well for England but could not save their side from defeat. The 33 extra runs, including 23 wides, also cost England dearly.
Bangladesh`s chase could not have started better as the openers raised a-run-a-ball 52 stand with Tamim Iqbal playing a quick-fire 38-run knock.
Iqbal was cleaned up by Bresnan in the ninth over and his side suffered two more jolts in form of Junaid Siddique (12) and Raqibul Hasan (0) within 30 balls.
Imrul Kayes (60) though was rock solid on the other end and was well supported by his skipper Shakib Al Hasan (32) as they raised 82 runs for the fourth wicket.
The runs came in singles and twos and there was a time in their partnership when not even a single boundary was scored in nine overs. Yet, importantly for the hosts, the scoreboard was ticking and the asking run-rate was never out of reach.
Kayes raised his seventh half-century with a single off James Anderson and then ended the boundary drought with a cover drive off Ravi Bopara. With that boundary he became only the 17th Bangladeshi batsman to score 1000 ODI runs.
However, the well-set Kayes ran himself out when he attempted a double, which never was, and that brought a twist in the match, with England now hoping for a turnaround.
At that stage, Bangladesh needed 71 runs from 114 balls but wickets fell in a heap after that.
Skipper Hasan edged one off Graeme Swann onto this stumps and paceman Ajmal Shahzad bowled Mushfiqur Rahim (6) and Naeem Islam (0) to reduce Bangladesh to 166 for seven.
Swann took his second wicket when he had Abdur Razzak caught by Tim Bresnan, much to the shock of the home crowd, but Shafiul hit the same bowler for a four and six to bring back the match alive.
Bangladesh took the final powerplay in the 46th over needing 33 from 30 balls. James Anderson leaked 11 runs in the first over of the powerplay which he started by bowling wide.
Mahmudullah suppported Shafiul well with his sensible batting and hit the winning boundary four off Bresnan, sparking wild celebration at the packed stadium.
Earlier, Jonathan Trott (67) and Eoin Morgan (63) hit fifties and shared a 132-ball 109-run fourth-wicket stand to save England the blushes as they were struggling at 53 for three at one stage
The 24-year-old Morgan, drafted in the team as a replacement for Kevin Pietersen, hit eight fours en route to his 72 ball knock, while Trott`s innings came off 99 balls with two fours.
England, however, lost their way, suffering another collapse in the face of a disciplined Bangladeshi bowling and lost their last six wickets for just 63 runs.
Naeem Islam, Abdur Razzak and skipper Shakib Al Hasan accounted for two wickets each, while Rubel Hossain, Shafiul Islam and Mohammad Mahmudullah got one apiece.
Sent into bat, wicketkeeper batsman Matt Prior walked out with skipper Andrew Strauss to open the England innings and combined for a 32-run partnership before losing his wicket in a bizarre fashion in the seventh over.
Strauss, too, was dismissed in the 11th over with Junaid Siddique taking a brilliant catch at slip off Naeem Islam. A lot was expected of Ian Bell but the right-handed batsman became Mohammad Mahmudullah`s victim as England slipped to 53-3 in 16.4 overs.
However, Trott and Morgan steadied the ship, adding 109 runs to lift England to 162.
The duo shrugged extravagance and toiled hard on the field, taking singles and twos to keep the scoreboard ticking.
Morgan, who is returning from an injury, picked up his first boundary in the 21st over when he lofted Mahmudullah over mid-wicket, before welcoming skipper Shakib Al Hasan with a boundary over mid-off.
The left-handed batsman showed excellent footwork and sent Mahmudullah for another four over midwicket, before pulling him along the carpet for another boundary.
Trott picked his first boundary in the 28th over off Rubel Hossain, bisecting the fine leg and deep square boundary. Morgan, meanwhile, swept Islam for another four, before using his feet to good result against Rubel.
In the 35th over, Morgan brought up his fifty with a single off Shafiul Islam, while Trott cantered to his individual half-century in the next over.
However, Naeem Islam brought Bangladesh back into the game, removing Morgan in the 39th over with Imrul Kayes taking a brilliant diving catch running in from deep fine leg.
After the 41st over, England took their batting powerplay but couldn`t utilise the five overs. With pressure mounting, Trott went for a big shot and holed out at long off to trigger another collapse.
Graeme Swann and Paul Collingwood took England across the 200-mark but, in pursuit of quick runs, wickets kept tumbling, as Bangladesh held things back in the end.