Bangladesh 32 for 2 (Tamin 21) trail Ireland 214 (Tector 50, Taijul 5-58) by 180 runs
Dhaka: Andy McBrine took a wicket with the final ball of the opening day of the Test to leave Bangladesh 34-2 after Ireland were bowled out for 214.
Harry Tector's half-century helped the Irish to 122-3 in Mirpur but they added just 92 more runs with Taijul Islam taking an impressive 5-58.
Mark Adair bowled Najmul Hossain Shanto for a duck as Bangladesh replied to a modest Irish total.
Fellow opener Tamim Iqbal reached 21 before falling to McBrine's last ball.
Bangladesh beat the Irish 3-0 in the ODI series and 2-1 in the T20s before the start of the one-off Test encounter at the Sher-e-Bangla National Cricket Stadium.
Ireland won the toss and elected to bat first, but they slipped to 48-3 before Tector (50) - making his maiden Test half-century - steadied the innings alongside Curtis Campher (34) in an Irish record fourth-wicket Test partnership of 74.
Tector was bowled by Mehidy Hasan as Ireland lost three wickets for only two runs to give Bangladesh control of the game.
Lorcan Tucker (37) and Adair (32) added valuable runs before both falling to Taijul while Mehidy and Ebadat Hossain both picked up two wickets.
It was a small total to defend but Adair gave the Irish a good start before McBrine's late show ensured Ireland finished the day on a high.