Earlier in the day, Bangladesh declared their first innings at a commanding 587 for 8, built on superb batting performances from their top order.
Mahmudul Hasan Joy missed out on a double hundred but laid the foundation with a superb 171, while Mominul Haque supported him well with 82.
Captain Najmul Hossain Shanto added a fluent 100, and Liton Das played a brisk knock of 60 to help stretch the lead beyond reach.
The morning session began well for Ireland as they dismissed Joy early on Day 3. Andy McBrine struck in his second over, with Joy edging behind to wicketkeeper Lorcan Tucker for 171.
His fine innings came off 286 balls, laced with 14 fours and four sixes, and ended a 173-run stand with Mominul.
Mominul soon followed, edging McBrine to slip after a well-made 82 off 132 balls. His innings, which included five fours and two sixes, ensured Bangladesh maintained a strong scoring rate despite the early losses. At that stage, the hosts were 346 for 3, firmly in command.
Shanto and Mushfiqur Rahim then rebuilt the innings with patience and control. The pair added 79 runs before Mushfiqur fell to young spinner Matthew Humphreys for 23.
Shanto, however, continued to score freely, reaching his 100 from 114 balls with 14 fours before being trapped leg-before by McBrine.
Litton Das provided the late flourish, playing in his natural attacking style. He smashed 60 off 66 balls, reaching his 19th Test fifty. His partnership of 98 runs with Shanto kept the momentum alive as Bangladesh powered past the 500-run mark.
After Shanto’s dismissal, Bangladesh soon declared their innings at 587 for 8, a total that virtually batted Ireland out of the contest. The visitors’ bowlers toiled hard, with McBrine picking up a few wickets but struggling to contain the flow of runs.
In reply, Ireland’s second innings got off to a disastrous start. The Bangladeshi bowlers struck regularly to reduce them to 86 for 5 by stumps.
With two full days remaining, Bangladesh now need just 5 wickets to secure an emphatic innings victory and take a 1-0 lead in the series.
