Tamim Iqbal (31) and Mushfiqur Rahim (51 not out) took the hosts nearer to their goal in a effective morning session as they crossed the end line on a deteriorating wicket quickly after lunch.
It was their first Take a look at win since defeating New Zealand at Mount Maunganui the earlier 12 months.
Eire, with six debutants and enjoying a Take a look at match for the primary time since 2019, made their highest first innings complete of 214 after opting to bat on the primary day, with Harry Tector scoring 50.
Bangladesh ran by Eire’s line-up on Taijul Islam’s eleventh five-wicket haul and posted a mammoth 369 in reply, using on an excellent 126 from Mushfiqur and 87 from captain Shakib Al Hasan.
However hosts Eire had been left dissatisfied after a 27–4 begin on the third day.
Tector was dropped early on at 9 and did many of the harm to hit one other half-century (56), whereas fellow debutant Lorcan Tucker made 108 earlier than Eire reached 286–8 at stumps and the competition lengthened with a lead of 131.
Andy McBrine, who took 6-118 to dismiss Bangladesh and in addition impressed with the bat in Eire’s second essay, added just one extra run to his in a single day tally to fall for 72 on the fourth morning as his staff ultimately made 292. However restricted.
Eire will play two Checks in Sri Lanka later this month.