The visitors picked up 13 wickets on the final day, led by spin all-rounder Sajid Khan, to seal the win at Mirpur's Sher-e-Bangla National Stadium on Wednesday even after rains washed out two and a half days of play.
After electing to bat, Pakistan declared at 300/4 in their first innings with skipper Babar Azam topscoring with 76.
In response, the Tigers were rolled for 87 in their first innings with off-spinner Sajid taking eight wickets.
Pakistan subsequently enforced the follow-on but the hosts could only muster 205 runs in the second innings, thanks largely to Shakib Al Hasan's 63. Sajid was once again the pick of the bowlers for Pakistan as he picked up four more wickets.
He finished with a career-best return of 12 for 128 to cap a man-of-the-match display.