England started well after Eoin Morgan won the toss and chose to bowl, with James Anderson taking two early wickets.
But Mahmudullah’s 103, along with fantastic support from Mushfiqur Rahim (89 off 77 balls), propelled them to a tough target, albeit on a good batting surface in Adelaide.
England made two changes to their team for the win-or-go-home game, with Alex Hales coming in for Gary Ballance as expected and Chris Jordan replacing Steven Finn in the bowling department.
But it was Anderson (2-45) who provided the early breakthroughs – 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 has so desperately needed.
Morgan was attacking with his fields early on as three slips were kept in place for the majority of the first 10 overs but Mahmudallah and Soumya Sarkar (40), in particular, played some lovely shots in an 86-run partnership that rebuilt the Bangladesh innings.
It was Jordan (2-59) who made the breakthrough in the 21st over, getting Sarkar caught behind with a bouncer brushing the batsman???s glove – a demonstration of his knack of picking up wickets despite also being expensive.
Moeen Ali (1-44) – who bowled well during his nine overs which will give encouragement to Bangladesh’s vast array of spinners – accounted for the ever-dangerous Shakib Al Hasan for just two the following over as again England benefitted from a double strike.
But he was then removed from the attack and the seamers bowled too short to Mushfiqur in particular, a move which looked to be a specific plan to the diminutive wicketkeeper-batsman.
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 Chris Woakes – two overs after he???d brought up his first hundred in ODI cricket, and Bangladesh???s first at a World Cup.
But Bangladesh somewhat lost their way thereafter as only 38 runs were added from the final five overs, with England bowling with good control at the death for the first time in the tournament.
Broad (1-52) picked up the wicket of Mushfiqur and Jordan in particular showed why his death-bowling expertise perhaps earned him the nod over Finn, with a wicket – Sabbir Rahman (14) and only three runs coming from the 49th over.
Ten runs were added from Woakes’ final over though to take Bangladesh to 275-7 to set England a testing total to chase under lights, with anything but a win seeing them eliminated from the World Cup.