Chasing 185 to win, the visitors inched their way to the target for the loss of four wickets, 25 minutes before tea on the fifth and final day to complete a 2-0 series sweep.
Bangladesh skipper was a notable contributor in the modest chase with 38 runs.
Earlier on Day 5, Zakir Hasan and Shadman Islam resumed their innings at 31 and nine respectively with Bangladesh needing 148 runs to sweep the series.
Mir Hamza gave Pakistan their first breakthrough as he castled Zakir after he played a quick knock of 40 off 39 with the help of three boundaries and two sixes.
Shadman soon followed his partner after scoring 24 as he fell prey to Khurram Shahzad.
However, Najmul Hossain Shanto and Mominul Haque fought back with an unbeaten 52-run stand to drag the total to 122-2 when the Lunch was called.
Prior to that, Hasan Mahmud led the bowling attack with his maiden five-wicket haul to help Bangladesh bundle Pakistan for a meagre 172 in the second innings on Day 4.
All-rounder Salman Ali Agha
Wicketkeeper batter Mohammad Rizwan and all-rounder Salman Ali Agha offered some resilience with their gutsy 43 and 47 knocks before the home side was booked on a modest total.
Other than Mahmud Hasan, Nahid Rana was the key bowler for Bangladesh with four wickets.
Prior to that, Khurram Shahzad took 6-90, while Mir Hamza and Salman Ali Agha bagged two wickets each to book Bangladesh for 262 in their first innings.
Khurram and Mir’s new ball spell left Bangladesh reeling at 26-6 before Lunch on Day 3, however, Litton Das and Mehidy Hasan Miraz helped the side recover.
They stitched a partnership of 165 runs before Mehidy departed after scoring 78 runs from 124 balls with the help of twelve boundaries and one six.
Meanwhile, Litton carried the team with a gutsy century, scoring 138 runs from 228 balls with the help of 13 boundaries and four sixes.
Earlier on Day 2, Bangladesh bowlers bowled out Pakistan on 274, with Mehidy Hasan Miraz leading the pack.
Mehidy was the pick of the bowlers for Bangladesh with a five-fer, followed by Taskin Ahmed, who bagged three wickets. Nahid Rana and Shakib Al Hasan shared two wickets between them.
From Pakistan, Salman Ali Agha offered a notable fight against the momentum-filled Bangladesh bowling attack with his 54 off 95 deliveries, laced up with three fours and two sixes.
Prior to that, Shan Masood scored 57 off 69 deliveries, including two boundaries, while Saim Ayub played a 58-run knock that featured four fours and two sixes.
For the unversed, the opening day of the second Test between Pakistan and Bangladesh was called off due to persistent rain here on Friday.
Squads
Pakistan: Abdullah Shafique, Saim Ayub, Shan Masood (c), Babar Azam, Saud Shakeel, Mohammad Rizwan (wk), Salman Ali Agha, Abrar Ahmed, Mir Hamza, Mohammad Ali, Khurram Shahzad.
Bangladesh: Shadman Islam, Zakir Hasan, Najmul Hossain Shanto (c), Mominul Islam, Mushfiqur Rahim, Litton Das (wk), Shakib Al Hasan, Mehidy Hasan Miraz, Taskin Ahmed, Hasan Mahmud, Nahid Rana.