Mustafizur Rahman took four wickets before Hasan Mahmud held his nerve as Bangladesh beat Ireland by just five runs in the third one-day international at Chelmsford on Sunday.
Victory gave Bangladesh a 2-0 win, with one washout, in the three-match series.
Mustafizur, a 27-year-old left-arm quick, finished with fine figures of 4-44 from 10 overs, including several top-order batsman, as Ireland were held to 269-9 in reply to Bangladesh's 274 all out.
Ireland needed 10 off the final over only for Hasan to take two wickets.
Then, with six required off the last ball, Hasan's fine yorker hit tailender Craig Young on the boot to the delight of the Tigers' vocal fans at the headquarters of English county Essex.
Ireland were well-placed when needing 51 off nine overs with seven wickets in hand.
But Najmul Hossain, who hit a maiden ODI century in Bangladesh's three-wicket win on Friday, took his first wicket at this level to remove Harry Tector.
The in-form Tector, fresh from a career-best 140 on Friday, had made a brisk 45 when he pulled part-time bowler Najmul only for Liton Das to take a stunning diving catch low down as he ran in from wide of long-on.
"If I tell you we had the belief we'd win, I'd be lying," Bangladesh captain Tamim Iqbal, who top-scored for the Tigers with 69, told ESPNCricinfo.
"But cricket is a funny game, wickets fall and scoreboard pressure is bad to have. When 'the Fizz' got two wickets (Curtis Campher and George Dockrell), we thought we had a chance."
Ireland paceman Mark Adair took 4-40 to leave his side chasing a gettable target of 275 off 50 overs.
But despite opener Paul Stirling, captain Andrew Balbirnie and Lorcan Tucker all making fifties, no batsman was able to produce the match-winning innings Ireland needed.
Tuesday's washout, something Ireland hoped to avoid by moving the series to England, denied the Irish the 3-0 clean sweep they needed to secure automatic entry into this year's World Cup in India.
Balbirnie was left to rue Ireland's collapse on Sunday, saying: "We've played a lot of games in these atmospheres, we just need to be harsh on ourselves. One of us had to stay in and score a hundred."
Ireland, having missed out on a top-eight finish in the Super League, will now compete in the June 18-July 9 qualifying tournament in Zimbabwe.
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