Pakistan had won the first Test in Chittagong by an innings and 184 runs and by winning the second Test they improved their ICC Test ranking from sixth to fifth.
Chasing an easy target of 103 runs, Pakistan completed the second successive victory before tea break.
In the process, they lost openers Mohammad Hafeez (47) and Taufiq Umar (3) and one-down batsman Azhar Ali (34) while Younis Khan and skipper Misbah-ul-Haq remained unbeaten on 16 and six, respectively.
Earlier, Pakistan bowled out Bangladesh for 234 runs in the second innings an hour after lunch.
Pakistan made 470 in their first innings in reply to Bangladesh's 338.
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