Shorifull also broke the 41-run partnership between James Neesham and captain Mitchell Santner for the sixth wicket, which was their highest partnership of the match.
Mustafizur took the prized wicket of top-scorer Neesham, who scored 48 runs in 29 balls, taking the Kiwis to 110 for 7 in 16.3 overs.
The host team could ultimately score only 134 runs for nine wickets in 20 overs.
Shoriful Islam took 3 wickets for 26 runs in 4 overs. Mahedi and Mustafizur took two wickets each for 14 and 15 runs in their 8 overs.
This was Bangladesh’s fourth win over New Zealand in T-20.
Before the match, the Tigers played nine T20Is against the Kiwis in New Zealand and 11 T20Is overall in the country but did not achieve any wins.