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.
(Reporting by Sudipto Ganguly in Mumbai; editing by Douglas Beattie)
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