Set a challenging 276 to win and stay in the tournament after Mahmudullah (103) became the first Bangladesh batsman to score a World Cup hundred, England fell to 260 all out in another humiliating loss.
Jos Buttler (65 off 52 balls) tried valiantly to get England over the line after a dismal batting display saw the top order crumble to 163-6.
But Buttler fell with 38 still required with just over four overs remaining and though Chris Woakes??? impressive 42 off 40 took England to within 16 of the target, he ran out of partners at the other end with Chris Jordan in particular falling to a contentious run-out decision.
It means England are out of the World Cup with one game still to play, a now dead rubber against Afghanistan on Friday.
England started well after Eoin Morgan won the toss and chose to bowl, with James Anderson (2-45) taking two early wickets ??? his usual probing line on off-stump drawing the edge of both Imrul Kayes and Tamim Iqbal for two.
With only eight runs on the board and Jordan having dropped Iqbal off Stuart Broad a few balls before his eventual departure, it looked like England might be well set for the kind of convincing performance their tournament so desperately needed.
But Mahmudallah and Soumya Sarkar (40), in particular, played some lovely shots in an 86-run partnership that rebuilt the Bangladesh innings.
Chris Jordan (2-59) ??? on his World Cup debut ??? made an initial breakthrough in the 21st over, getting Sarkar caught behind with a bouncer brushing the batsman???s glove, before Moeen Ali (1-44) accounted for the ever-dangerous Shakib Al Hasan for just two the following over as England again benefitted from a double strike.
But he was then removed from the attack and the seamers bowled too short to the new batsman, Mushfiqur in a move which looked to be a specific plan.
It didn???t work though as he and Mahmudullah benefited from the line of attack with another big partnership adding to the scorecard as Bangladesh moved from 99-4 to 240-5 in the 46th over.
The wicket was that of Mahmudullah ??? run out by Woakes ??? two overs after he???d brought up his first hundred in ODI cricket, and Bangladesh???s first at a World Cup.
Bangladesh somewhat lost their way thereafter as only 38 runs were added from the final five overs ??? Broad (1-52) picking up the wicket of Mushfiqur and Jordan accounting for Sabbir Rahman (14).
It left a testing target of 276 to chase under lights but on a good pitch and England???s openers got off to a great start, cruising to 43-0 after seven overs before a shambolic run-out saw Moeen Ali (19) depart two balls later.
He was inching down the track looking for a quick single but with Ian Bell guilty of ball watching, Moeen was left stranded when trying to dive back home to safety.
It was the kind of unnecessary dismissal which would litter England???s innings as first Alex Hales (27) edged the military medium pace of Bangladesh captain Mashrafe Mortaza through to Mushfiqur behind the stumps, having looked nicely set during his first knock of the tournament.
Bell (63) went through to fifty but his wicket ??? another disappointing effort from the Warwickshire man having again used up too many deliveries in the middle overs ??? brought about a mini-collapse of three wickets for 11 runs.
He tried to uppercut a hostile Rubel Hossain bouncer which reared up on him and only succeeded in guiding it through to Mushfiqur.
Three balls later England were in turmoil when their captain Morgan picked out the man in the deep when going for the big shot with scoreboard pressure mounting.
And James Taylor???s dismissal was perhaps the tamest of the bunch, merely offering catching practice to Kayes at slip when wafting at a wide one from Taskin.
Buttler played a magnifect hand, displaying the kind of calm and clean hitting at the crease that was lacking from the top order.
He put on 31 runs with Joe Root (29) before he fell just after the batting powerplay was enforced in the 36th over ??? Mortaza again bringing himself back into the attack and again making the breakthrough with Root getting a thin edge through to Mushfiqur.
But it was his partnership with Woakes, that had England sniffing an unlikely victory, with 75 added from 61 balls, though Buttler???s wicket ??? another dismissal through to Mushfiqur ??? when looking to run the ball down to third man, and Jordan was very harshly run out the next ball to all but extinguish hopes of the win.
Jordan made his ground when scrambling back for his crease but the bat bounced in the air and with the third umpire deciding that nothing was grounded when the bails were dislodged he was given out, although replays seemed to be inconclusive.
Stuart Broad hit a big six and Woakes was dropped by Tamim to suggest the match wasn???t perhaps quite over yet but Rubel cleaned up Broad and Anderson, bowling both in the penultimate over to seal a famous win for Bangladesh.