
Liton struck a team-high 128 off 192 balls, an innings lacedwith eight fours and four sixes. Mushfiqur, who reached the rare milestone of scoring a century in his 100th Test, made 106.
Mominul Haque added 63 while Mehidy Hasan Miraz contributed a valuable 47 to help Bangladesh set a formidable total.
Offspinner Andy McBrine produced a remarkable spell of bowling to deny Bangladesh a 500-plus score, finishing with career-best figures of 6-109.
Bangladesh resumed the day on 292-4, with Mushfiqur completing his century in the ninth delivery of the morning. Having been stranded on 99 overnight, he calmly nudged Jordan Neill for a single to raise his 13th Test hundred, made off 195 deliveries.
He had earlier survived a close appeal before safely negotiating a maiden over from left-arm spinner Matthew Humphrey at the start of the day.
Humphrey eventually ended Mushfiqur's stay, breaking a 108-run stand and claiming Ireland's only wicket of the morning session.
Liton continued his fluent batting, reaching his fifth Test century - and his first since the Rawalpindi Test against Pakistan in 2024 - from 158 balls, delicately paddling Gavin Hoye to the fine-leg boundary.
Miraz offered solid support in a 123-run sixth-wicket partnership, but Ireland clawed back by removing both batters within the space of four deliveries. Hoye, who finished with 2-115, dismissed Miraz, while Humphrey removed Liton to complete a haul of 2-151.
McBrine then returned to clean up the tail, taking the wicket of Hasan Murad before trapping Khaled Ahmed leg-before to wrap up the innings, reports BSS.