Bangladesh were 205 all out, A. Botha 3-32 while Ireland could reach at the total of 178 runs Shafiul Islam took 4 wickets.
Earlier Ireland bowled out Bangladesh for a modest 205 runs in their Group B clash as a sell-out home crowd of 25,000 looked on in stunned silence.
Seamer Andre Botha picked up three wickets and George Dockrell and Trent Johnston claimed two each after the home side elected to take first strike on a slow pitch at the Sher-e-Bangla stadium.
Wickets tumbled at regular intervals in a match Bangladesh had targeted as a must-win after they lost their first match to India by 87 runs at the same venue last week.
The hosts made a blistering start, racing to 49 without loss by the end of the fifth over, 37 of those runs coming from the blade of Tamim Iqbal. But the advantage was soon lost as four wickets fell for 33 runs in the next 10 overs.
Imrul Kayes was stumped brilliantly by Niall O’Brien off a John Mooney wide, Junaid Siddique was run out by a direct throw from Ed Joyce and Tamim holed out to point off Botha.
Tamim, who top-scored with 70 against India, began by taking 10 runs in Boyd Rankin’s opening over and stroked seven boundaries in his 44 off 43 balls.
Bangladesh skipper Shakib Al Hasan had made a fluent 16 when he patted the ball back to bowler Botha after being dropped by his Irish counterpart William Porterfield at point in the previous over.
Mushfiqur Rahim and Raqibul Hasan lifted the hosts with a 61-run stand for the fifth wicket but Bangladesh then suffered twin blows at the hands of left-arm spinner Dockrell.