Sohail Tanveer (3-29), Rao Iftikhar (2-16) and Shahid Afridi (3-40) shattered the tourists' batting as they folded at 129 in 29.5 overs to give Pakistan a 1-0 lead in the five-match series.
Tanveer rocked Bangladesh with a triple strike in his incisive seven-over spell, removing Tamim Iqbal (five), Shahriar Nafees (24) and Aftab Ahmed (14) to leave the visitors reeling at 49-3.
Two power breakdowns, stopping play for 48 minutes in all, saw Bangladesh's target revised to 282 in 39 overs which proved beyond their reach after a poor start.
Iftikhar had Bangladesh skipper Mohammad Ashraful (nine) and Shakib Al Hasan (nought) to further compound the tourists' problems.
Leg-spinner Shahid Afridi (3-41) then removed Farhad Reza (seven) and Dhiman Ghosh (nought) while Shoaib Malik dismissed Roqibul Hassan (12) to bring Pakistan closer to victory.
Mashrafe Mortaza (25) and Abdur Razzak (11 not out) shared 37 for the last wicket to take Bangladesh past 100 but it only delayed the inevitable.
Earlier, Mohd Yousuf crafted a fine 108* and Malik made a strokeful 85 as Pakistan posted a mammoth 322/5 in the first of the five-match ODI series against Bangla at the Gaddafi Stadium in Lahore on Tuesday.
Yousuf and Malik revived Pak innings with a run-a-ball 145-run stand for the fourth wicket after Bangla opening attack Reza and Mortaza struck in regular intervals to leave hosts reeling on 70/3.
Yousuf's 103-ball knock was inclusive of 11 hits to fence while Malik belted 7 boundaries.
Misbah (38 off 27 balls) and Afridi ( 27 off 11, 2X4s&2X6s) played a little cameo innings in the final overs to take Pak past 300 runs.
Bangla new-ball bowlers Mortaza and Reza bowled exceptionally well on a unforgiving lahore strip to return with 2/52 and 2/41 respectively.