Shakib Al Hasan and debutant Towhid Hridoy both narrowly missed centuries but Bangladesh still hammered Ireland's attack to post 338-8 in Saturday's first of three one-day internationals in Sylhet.
Shakib hit 93 and Towhid added 92 as the pair added 135 for the fourth wicket to lift Bangladesh from 81-3 after Ireland captain Andrew Balbirnie won the toss and elected to bowl.
Graham Hume claimed a career-best 4-60 but the hosts did well enough to post their highest one-day score against Ireland.
Shakib led the initial charge after Tamim Iqbal (3), Liton Das (26) and Najmul Hossain (25) fell cheaply.
He became the second Bangladeshi cricketer to reach 7,000 ODI runs after Tamim.
Shakib is now also just the third cricketer to surpass that milestone in ODI runs and 300 one-day wickets after Sri Lanka's Sanath Jayasuriya and Pakistan's Shahid Afridi.
Shakib shifted gears after reaching his third successive ODI fifty and hitting Harry Tector for five fours in an over.
He fell seven runs short of his 10th ODI hundred after chasing a wide yorker from Hume to get the bottom edge.
Towhid played the best debut innings for Bangladesh in ODIs, adding 80 runs for the fifth wicket with Mushfiqur Rahim, who struck 44 off 26 balls.
Hume removed both batsmen in the same over before taking the wicket of Taskin Ahmed but the tourists were unable to stop the flow of runs.