Afghanistan batted for 142 overs in their second innings, 92 on Tuesday's fifth and final day, to force a sensational draw.
The host side in Abu Dhabi began the day on 3-132, lost five more wickets, but fought on to hold out to stumps at 8-346.
Bangladesh dominated the match after winning the toss and batting first.
Bangladesh earned a first-innings lead of 106 runs after dismissing Afghanistan for 240 with Hasan Mahmud taking 5-55 and a hat-trick.
They then declared the second innings at 7-372 after player-of-the-match Litton Das was out for 102. That gave Bangladesh an imposing lead of 478 and four-and-a-half sessions to bowl out Afghanistan.
But Afghanistan defied the odds despite losing two wickets in the first seven overs on Monday.
Opener Atal, in his third Test, ate up most of the chase as he faced 332 balls over more than eight hours to score 111. Ismat Alam also exemplified Afghanistan's defiance batting 60 balls for four, not scoring until his 45th.
Atal was finally was caught close to the wicket after tea, the seventh man out. Afghanistan still had 23 overs to survive with tailenders left.
But 34-year-old Yamin Ahmadzai, who inside-edged a ball onto the stumps only for the bails to stay put, faced 85 balls for a career-best 19. Qais Ahmad, who has played franchise cricket in eight countries, faced 80 to finish with an unbeaten career-best 49.
Ahmad was dropped on 29 by Mahmud and made the ending more dramatic when he collapsed clutching his left hamstring. He soldiered on and finished the match with a six over mid-wicket.
Bangladesh wicketkeeper Das set a new record of nine dismissals, a century and a half-century in the match. He could have had one more dismissal but he missed a difficult stumping of Atal when the batter was on 70.
Atal, resuming on 35 overnight, became the first Afghan batter to score a century in the fourth innings of a Test after he pulled Mehidy Hasan Miraz to the boundary as Bangladesh struggled to get through the defence of the elegant left-hander.
His was the seventh longest innings in the fourth innings of a Test and the first by an Afghan in the fourth innings.
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