England's calamitous World Cup campaign suffered its final indignity as a 15-run defeat to Bangladesh sent them crashing out of the tournament amid controversy in Adelaide.
Morgan's decision to bowl after winning the toss was immediately rewarded when Anderson removed openers Imrul Kayes and Tamim to catches in the slip cordon in his first two overs.
Imrul edged the fourth ball of the day to Jordan at third slip before Tamim offered a regulation chance to Joe Root. In between Tamim had already survived a Jordan dropped catch diving to his left.
England's change bowlers failed to maintain the early pressure, however, and Mahmudullah was able to ease his side's early discomfort in an 86-run stand alongside Soumya Sarkar.
Moeen Ali removed the dangerous Shakib, caught by Root at slip, and Bangladesh were 99 for four. Morgan reinserted Broad as he sensed an opening and the diminutive Mushfiqur Rahim targeted early on with some short-pitched bowling.
Mushfiqur did most of the risk-taking, as he rattled along at just over a run-a-ball, but Mahmudullah was rewarded for his graft with his first century after 114 ODIs. It came from 131 balls, with seven fours and a pair of sixes, but a Woakes direct-hit from short third-man prevented him from going on for more.
Ian Bell had looked to pace the pursuit with 63 from 82 balls, but slashed behind before skipper Eoin Morgan then followed when he pulled straight to Shakib on the square-leg rope for a duck – his fifth in nine innings.
Mahmudullah's maiden ODI century proved critical after Anderson had given England a dream start with two wickets in his first two overs.
England appeared resigned to their fate when Joe Root edged behind and they were 163 for six.
Buttler was left with no recognised batsman to partner and a required rate spiralling past nine runs an over. The 24-year-old revealed none of the nerves that had racked those before him, however, as he instead displayed the power and invention that has marked him as England's most eye-catching talent.
He brought his half-century up from 41 balls and, with Chris Woakes looking similarly assured, they stole the momentum away in a 75-run stand from 61 balls. But the game took another twist when Buttler edged Taksin Ahmed behind with 38 still needed and then Jordan was controversially given out.
Jordan had reached beyond the crease but TV umpire Simon Fry felt his bat had bounced up into the air as Shakib Al Hasan's throw hit the stumps.
There was yet more drama as Woakes was dropped in the deep by Tamim Iqbal and Stuart Broad crashed a six. But Rubel finished the game off as he bowled Broad and then yorked Anderson to spark Bangladeshi celebrations as they reached the World Cup knockout stage for the first time.
The defeat will leave England coach Peter Moores with plenty of serious questions to answer in the coming days, when England will prepare for their final group game against Afghanistan in Sydney on Friday with nothing to play for.
