Pakistan won the toss and bowled first, reversing the trend of the first two matches which New Zealand won by nine and five wickets.
After New Zealand made 204, Pakistan finished at 1-207 with four full overs to spare to inflict New Zealand's heaviest T20 loss in terms of wickets.
Newcomer Nawaz - who debuted in this series with ducks in the first two matches - was supported in his maiden century by captain Salman Ali Agha, who made 51 from 31 balls in an unbroken second-wicket stand of 133.
"I failed in the first two games and I thank the team for backing me," he said through an interpreter. "When I went out to bat I wanted to score my first international run.
"After I scored the first run the pressure was released and I wanted to win the game."
Mark Chapman made 94 from 44 balls before New Zealand was bowled out with one ball remaining in their 20 overs. Chapman hit 11 fours and four sixes but lacked support.
Captain Michael Bracewell's 31 was the next-best effort by the Kiwis, who lost wickets regularly. Tim Seifert made 19, including 16 runs from the second over.
Haris Rauf took 3-29 in an excellent bowling performance in the middle of the innings.
The Pakistan selectors kept Nawaz and Mohammad Haris at the top of the order, giving them time to acclimatise to New Zealand conditions.
Their opening partnerships produced only one run in each of the first two matches. But on Friday they put on 75 for the first wicket, within the six-over power play.
Haris made 41 from 20 balls with four fours and three sixes to get the Pakistan innings off to the rapid start it needed. He hit two sixes from the first over bowled by Kyle Jamieson as Pakistan rushed to 50 from only four overs.
Jamieson, who took 3-8 in the first match, conceded 30 runs from his first two overs.
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