Left-arm spinner Taijul Islam claimed 5-58 for Bangladesh on Tuesday to help bowl out Ireland for 214 but two early strikes left the one-off Dhaka test in the balance.
Bangladesh took to the crease not long after drinks and were 34-2 at stumps, with Andy McBrine sending back Tamim Iqbal for 21 on the last ball of the day.
Mark Adair bowled Najmul Hossain for a duck in the first over of the innings. Mominul Haque was unbeaten on 12 at the end of day's play with Bangladesh trailing Ireland by 180 runs.
Harry Tector earlier top-scored with 50 for the tourists, who otherwise struggled to build partnerships after electing to bat first.
Shoriful Islam struck early to trap opener Murray Commins for five before Ebadot Hossain and Taijul scalped James McCollum (15) and Andy Balbirnie (16) respectively.
Tector, one of Ireland's seven debutants for Ireland in their first test since July 2019, put on 74 runs with Curtis Campher for the fourth wicket to steady the innings, rescuing the side from a precarious 48-3.
"We had a bit of a ceremony last night. There was seven of us, so presenting seven individual caps on the morning of day one would take a bit of time," Tector said of the side's new blood.
"It is a very special achievement. We are a lucky group."
Mehidy Hasan Miraz bowled Tector to break the stand before Taijul made two quick strikes to dismiss Peter Moor (1) and Campher (34), derailing Ireland again.
Cameos from Lorcan Tucker (37), McBrine (19) and Adair (32) took the visitors past the 200-run mark.
Taijul trapped Adair leg-before to complete his 11th five-wicket haul in tests and Mehidy wrapped up Ireland's innings in the next over to finish with 2-43.
"Taking five wickets on such a pitch was a difficult task," said Taijul.
"Our target was to bowl according to line and length without panicking."
Ireland have lost all three of their previous tests since becoming a full member of the International Cricket Council in 2017.
BANGLADESH: Tamim Iqbal, Najmul Hossain, Mominul Haque, Shakib Al Hasan (capt), Mushfiqur Rahim, Liton Das, Mehidy Hasan Miraz, Taijul Islam, Ebadot Hossain, Khaled Ahmed, Shoriful Islam..
IRELAND: Murray Commins, James McCollum, Andy Balbirnie (capt), Harry Tector, Peter Moor, Lorcan Tucker, Mark Adair, Curtis Campher, Graham Hume, Andy McBrine, Ben White.