The win knocked out Suresh Raina's New York Lions from play-off contention.
New Zealand beat Bangladesh by 65 runs in a rain-shortened third Twenty20 International in Auckland on Friday to claim a series clean sweep.
James Pattinson had to run a long distance before grabbing the ball while diving forward to send Todd Astle packing.
New Zealand didn't do themselves any favours as Australia piled on the misery on Day 4 of the third and final Test.
New Zealand brought in all-rounder Jimmy Neesham and leg-spinner Todd Astle after losing the five-match series on Monday.
New Zealand pulled off a dramatic win by an innings and 49 runs over England in Auckland on Monday, wrapping up the rain-affected first Test with 18.5 overs to spare.
Todd Astle made his solitary appearance for New Zealand in a Test against Sri Lanka in 2012 and has yet to play a one-day or Twenty20 international.
It was an impressive performance by the Kiwis considering the conditions and the opposition.
Uncapped Todd Astle has been included in New Zealand's squad for its cricket tour to Sri Lanka. Astle, from Canterbury province, averages 22 with the bat in New Zealand's domestic first-class competition and has taken 127 wickets at 34.79 with his leg breaks.