After off-spinner McBrine had claimed the last two home wickets for figures of 6-109, Ireland were left with 38 overs to respond to an imposing 476 all out, containing centuries by Mushfiqur Rahim and Litton Das.
The visitors began well, with veteran openers Andy Balbirnie and Paul Stirling adding 41, but the innings started to fall apart after the latter was adjudged lbw for 27, halfway down the pitch.
Ireland have been quick learners at the five-day game, winning three of their first 10 Tests (it took Bangladesh 35 matches to record a victory) but if they have an Achilles heel it would seem to be the inability to dig in after long sessions in the field.
While no blame can be attached to Stirling, who hit one meaty six into the stands at mid-wicket, Balbirnie’s lack of foot movement led to him edging to slip and after a couple of leg-side boundaries, Cade Carmichael was lbw.
Enter Curtis Campher, who was surely batting two places too high with Stephen Doheny in the XI. Exit Campher four balls later, bowled for nought.
Harry Tector battled for 34 balls for 14 before he played back to left-arm spinner Taijul Islam and was lbw for the third time in three innings on tour, leaving Lorcan Tucker and Doheny to see out the final five overs before trudging off with 98-5 on the board.
The trio of Ireland spinners can feel let down by their batters after getting through 117.1 overs in the heat.
Leg-spinner Gavin Hoey took his first two Test wickets, Matthew Humphreys also claimed two, as reward for a marathon 50 overs, and McBrine was the most valuable player in the team.
The question for day three is not if Ireland will save the follow on but whether Bangladesh will enforce it.
Or maybe it isn’t. Because the last time Ireland collapsed in Mirpur, Tucker dominated most of the next day, making his maiden century, and McBrine, who has yet to bat, made a dogged 72.
Can history repeat itself?