Chasing 185 to win, the visitors inched their way to the target 25 minutes before tea on the fifth and final day to complete a 2-0 series sweep.
Bangladesh achieved the target for the loss of four wickets with Zakir Hasan (40), captain Najmul Hossain Shanto (38) and Mominul Haque (34) the main run-scorers.
Mushfiqur Rahim (22*) and Shakib Al Hasan (21*) brought the tourists home to spark jubilation among the visiting squad.
Bangladesh won the first Test, also in Rawalpindi, by 10 wickets for a landmark first victory over Pakistan in 14 matches.
Pakistan scored 274 and 172 in the second Test while Bangladesh recovered from 26-6 to make 262 in their first innings.
Litton Das’ 138 rescued Bangladesh with the bat before fast bowlers Hasan Mahmud (5-43) and Nahid Rana (4-44) wrecked Pakistan on Monday.
This is only Bangladesh’s third away series win in 33 attempts, having also beaten the West Indies in 2009 and Zimbabwe three years ago.
© Agence France-Presse
Photo: @BCBtigers/X