Bangladesh fell 28 runs short of their revised target of 171. Despite efforts from Soumya and Mahmudullah, the score proved to be too big to chase for the visitors.
They ended up scoring 142/7. Southee, Bennett and Milne each took 2 wickets and Glen Phillips took the other one.
Phillips was awarded the player of the match. New Zealand won the T20I series after Tests and ODIs.
Bangladesh lost Mahmudullah, Afif and Mithun within five deliveries.
Mahmudullah and Afif were bowled out by Milne. Mithun gave catch to Conway facing Southee.
The visitors still need 45 runs from 10 deliveries.
Naim was picked up by Guptil at long-off while trying to go inside-out on Phillips. He departs after scoring 38 runs from 35 balls.
Bangladesh require 60 from 24 balls.
Soumya was trapped by Milne facing Southee shortly after a 25-ball century. He had scored 51 from 27 deliveries.
Bangladesh still needs 76 runs from 6 overs.
Except losing early wicket of Liton Das, Bangladesh batsmen have shown resilience as they scored 76/1 in six overs.
Soumya Sarkar scored a blazing 40 from 15 balls. He hit three sixes to reach the figure. Naim is accompanying him with 26 runs from 23 deliveries.
Liton gave an easy catch to Phillips facing Bennett after scoring 6 runs.
After the heavy rain, New Zealand's innings drew to a close and as per the D/L method, Bangladesh need to chase 170 in 16 overs to win.
The visitors are currently at 6/0. Liton Das and Mohammad Naim have opened for the Tigers.
Rain again disrupted the game and the New Zealand innings might be abandoned. Should it happen, Bangladesh need to make 179 runs within 17 overs as per the Duckworth Lewis method.
Despite losing the wicket of Mark Chapman, the hosts thrashed Bangladesh bowlers to score 173 runs in 17.5 overs.
Phillips picked up a stunning 27-ball fifty and still not out at 58 runs from 31 balls. DJ Mitchel scored 34 from 16 deliveries.
Mahedi took the wicket of Chapman at 111 runs.
The match resumed after a short pause.
New Zealand have scored 108/4 in 13 overs.
The umpires have called for covers as rain disrupted the game.
New Zealand lost their fourth wicket after Mahedi lured Young with a loopy length ball and subsequently getting him stumped by Liton. He made 14 runs from 17 balls.
Despite the loss, the hosts have scored past 100 comfortably with Glenn Phillips at the helm. He scored a blazing knock of 30 from 17 balls.
The Kiwis are at 102/4.
Shortly after Guptil's departure, Conway sent to Pavillion too by Shoriful as Bangladesh comes back to the game all guns blazing.
Conway edged the ball to deep square to Mithun after scoring 15 from 9 balls.
New Zealand is now at 55 runs at the cost of three wickets.
Another brilliant catch by Taskin gave Bangladesh a much-needed breakthrough. Saifuddin broke the partnership by picking up dangerous Guptil.
Bowling full on the pads Saifuddin forced Guptill to play the pick up shot which ended up with a thick inside edge. Taskin plucked a one-handed stunner.
Guptil departs after scoring 21 from 18 balls. New Zealand are at 55/2.
The New Zealand side are cruising smoothly on the second T20I in Napier after losing the toss.
They are 40 for 1 after 5 overs. Fin Allen was the only man to depart after mistiming Taskin and outstanding effort from Mohammad Naim.
He made 17 runs facing 10 deliveries. Martin Guptil is at the crease with 20 from 16 balls on board.
New Zealand XI: Martin Guptill, Finn Allen, Devon Conway (wk), Will Young, Glenn Phillips, Mark Chapman, Daryl Mitchell, Tim Southee (capt), Ish Sodhi, Hamish Bennett, Adam Milne
Bangladesh XI: Liton Das (wk), Mohammad Naim, Soumya Sarkar, Mohammad Mithun, Mahmudullah (capt), Afif Hossain, Mohammad Saifuddin, Mahedi Hasan, Nasum Ahmed, Shoriful Islam, Taskin Ahmed