Ebadot Hossain took Ireland's two final wickets to leave Bangladesh a chase of 138 in Friday's fourth day of the one-off test in Dhaka.
The tourists added just six runs to their overnight 286-8 after Ebadot forced last man Graham Hume to give a catch behind the stumps for 14.
Andy McBrine added just one run to his overnight 71 to give Ebadot a finish of 3-37.
Ireland were staring down the prospect of an innings defeat on Thursday before debutant Lorcan Tucker's 108 made him only the side's second test centurion.
Harry Tector added 56 to lift Ireland from a precarious 13-4 and surmount a 155-run first innings deficit.
The visitors were all out for 214 runs in their first innings and in response, Bangladesh posted 369 runs.
Ireland have lost all three of their previous tests since becoming a full member of the International Cricket Council in 2017.
Source: SuperSport
BDST: 1201 HRS, APR 07, 2023
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