The visitors chased down Pakistan 178 with 10 balls to spare.
New Zealand levelled the two-match Test series 1-1 against Bangladesh by clinching victory in the second game within four days on Saturday.
With this, the Tigers take a 1-0 lead in the two-game series and have gained crucial WTC points.
Bangladesh is only three wickets away from registering their second Test win over New Zealand.
Kane Williamson (104) scripts record with brilliant hundred in Sylhet Test.
Mahmudul Hasan resilient knock of 86 off 166 balls provided Bangladesh with a solid foundation for a substantial total.