The Men In Green won the second consecutive T20I of a three-match series, taking the series 2-0.
Zaman struck an unbeaten 57 off 51 balls as Pakistan reached 109-2 in 18.1 overs after restricting Bangladesh to 108-7 in 20 overs.
Najmul Hossain earlier top-scored with 40 off 34 balls for Bangladesh while Afif Hossain chipped in with 20 runs from 21 balls.
Fast bowler Shaheen Afridi finished with 2-15 for Pakistan while leg-spinner Shadab Khan grabbed 2-22.
Pakistan won the first match of the series by four wickets on Friday.
The third and final match will be held at the same ground on Monday.