Mahmudulla shared a defiant 141-run stand with half century-maker Mushfiqur Rahim for a Bangladesh lineup aiming to reach its first World Cup quarterfinal and eliminate England in the process.
England must beat Bangladesh and then Afghanistan in its last two pool matches to have any chance of reaching the quarterfinals.
Eoin Morgan's decision to bowl first and field three slips brought immediate dividends when Jimmy Anderson had Imrul Kayes caught off the fourth ball, then dismissed Tamim Iqbal two overs later to have Bangladesh reeling at 8-2.
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Despite a return to form by seamer Anderson, Mahmudulla and Rahim played Soumya Sarkar and Mahmudullah then settled in to resurrect the Bangladesh innings, sharing an 86-run third-wicket stand until Chris Jordan (2-59) claimed his first World Cup wicket by having Sarkar caught behind for 40.
Despite a return to form by seamer Anderson (2-45), Mahmudullah and Rahim played some bold shots to salvage the innings.
Mahmudullah reached his historic hundred with a single before removing his helmet and blowing a kiss to a vocal section of Bangladeshis in the crowd, and accepting a hug from Rahim. Mahmudullah timed seven boundaries and two sixes in his 138-ball innings.
Rahim was closing in a hundred before being caught by Jordan at cover off Broad for 8
