Shakib Al Hasan hit the winning boundary 25 minutes before the tea break on the fifth and final day to spark jubilation in the away dressing room.
A handful of Bangladesh supporters waving the nation’s flag were also there to see their country win only a third away series in 33 attempts.
Shakib remained unbeaten on 21 and Mushfiqur Rahim was on 22 as the visitors painstakingly overhauled the tricky 185-run target.
Pakistan scored 274 and 172 while Bangladesh recovered from 26-6 to make 262 in their first innings.
Litton Das’s 138 rescued Bangladesh with the bat before fast bowlers Hasan Mahmud (5-43) and Nahid Rana (4-44) wrecked Pakistan on Monday with career-best figures.
Bangladesh won the first Test by 10 wickets — also in Rawalpindi — for their first victory over Pakistan in 14 matches.
Bangladesh outplayed the home team in both Tests and was the better bowling side despite having an inexperienced pace attack.
Before this, Bangladesh’s only away Test series wins came in the West Indies in 2009 and Zimbabwe three years ago.