Corey Anderson slammed an unbeaten 94 and added 124 with Williamson to lift New Zealand to 194.
Kane Williamson scored 60 to revive the New Zealand innings.
Soumya Sarkar (42) gave Bangladesh a brisk start in their chase.
Shakib Al Hasan (41) tried hard to resurrect Bangladesh's innings but they eventually fell short by 27 and conceded the series 0-3.
Williamson got rid of dangerous looking Sabbir Rahman to jolt Bangladesh.
Rubel Hossain struck twice as New Zealand slipped 55 for 3 in ten overs.
Jimmy Neesham gave New Zealand a solid start before he fell 15.
MOUNT MAUNGANUI, NEW ZEALAND - JANUARY 08: Corey Anderson of New Zealand bats during the third Twenty20 International match between New Zealand and Bangladesh at Bay Oval on January 8, 2017 in Mount Maunganui, New Zealand.