Ireland posted a competitive 4-181 in Thursday's opener thanks to a well-composed knock from Harry Tector, who remained unbeaten on 69 from 45 balls.
Chasing a challenging target, Bangladesh managed to put up 9-142 after a disastrous start, as they were reduced to 3-5 in the fourth over.
Despite a lone fight from Towhid Hridoy, who struck a career-best 83no, Bangladesh's batting collapse was too much to overcome.
Humphreys, who was impressive amid the tourists' 2-0 loss in the Test series, gave the side a breakthrough in the opening over by dismissing Tanzid Hasan Tamim for two, before taking three wickets in one over in his second spell to script Ireland's victory.
Mark Adair dealt a double blow to jolt Bangladesh further.
Adair sent back Parvez Hossain Emon and Liton Das, both for one in consecutive overs as he returned figures of 2-20.
Bangladesh tried to claw back into the game through Towhid Hridoy and Jaker Ali, who played patiently in order to rebuild the innings.
But pacer Barry McCarthy, who grabbed 3-23, undid Jaker with a short ball for 20, ending the 48-run partnership.
Humphreys returned with three wickets in one over, leaving Bangladesh at a precarious 8-74 in the 13th over.
Hridoy continued to fight, raising his fifth T20 half-century from 34 balls. He shared two partnerships with Shoriful and Nasum Ahmed to delay Ireland's victory.
Earlier, the knock by Tector, laced with one four and five sixes, drove the side to a challenging target for Bangladesh after the Irish openers gave the side a fluent start.
After being put in to bat, captain Paul Stirling and Tim Tector added 40 from 26 balls, before the captain top-edged a delivery of Tanzim Hasan Sakib for 21.
The Tector brothers — Harry and Tim — kept up the aggression until Tim Tector perished to a big shot after hammering a 19-ball 32.
After anchoring the innings, Harry Tector flourished in the last over, taking the total past 180.
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