Taijul Islam finished with six wickets as Bangladesh dismissed Pakistan for 358 to complete a 78-run win in the second Test and a 2-0 sweep of the series.
The left-arm spinner took two of the three wickets to fall on the final day and returned figures of 6-120 from 34.2 overs to help clinch the series.
The tourists were 7-316 on day four and added 42 runs on the fifth morning before losing the remaining wickets as Bangladesh rushed to victory.