Bangladesh, who also swept the three-match one-day international series, lost three quick wickets but chased down a 142-run target with 22 balls to spare, fired by an unbeaten 105-run stand between Shakib (57) and Sabbir Rahman (51).
Left-arm spinner Shakib was also miserly with the ball and gave away just 17 runs in his four overs as Pakistan posted 141-5 after Shahid Afridi won the toss and chose to bat.
Debutant left-arm paceman Mustafizur Rahman, 19, was the pick of the Bangladesh bowlers, picking up 2-20 in his four overs.
Mukhtar Ahmed (37), making a debut for Pakistan, and Ahmed Shehzad (17) added 50 in nine overs but the visitors failed to build on that strong platform.
Tamim Iqbal, Soumya Sarkar and Mushfiqur Rahim - the batting heroes for Bangladesh during the 3-0 ODI series win - all fell cheaply and it was left to Shakib and Sabbir to prop up their team after being reduced to 38-3.
The duo ensured the hosts maintained their winning streak with their first win in the shortest format of the game in eight matches against Pakistan.
Original source: Bangladesh smash Pakistan - again