The 18-run victory gave Pakistan a come-from-behind 2-1 series win that will see them overtake New Zealand at the top of the world rankings.
Captain Sarfraz Ahmed leapt with delight after the final ball as Pakistan pulled off back-to-back wins over the hosts.
Batting first on a friendly wicket, Pakistan reached 181 for six with Fakhar Zamanmaking 46 off 36 at the top of the innings. Umar Amin led a late charge that saw 58 runs scored in the final four overs.
New Zealand, in reply, were never up with the run chase, and managed 163 for six in their 20 overs.
The defeat followed a 48-run loss in the second game, after New Zealand swept the one-day series and won the first T20.
The consecutive defeats, following an unbeaten 13-match winning streak across all formats against the West Indies and Pakistan, put a dampener on New Zealand’s preparation for next month’s triangular series with Australia and England.
Zaman was the architect at the start of the Pakistan innings with a sharp 46 before being dismissed in a debatable decision when Tom Bruce took a catch at ground level.
Television replays were inconclusive on whether the ball touched the grass, and after lengthy deliberations the third umpire ruled in favour of the on-field decision.
New Zealand managed to arrest Pakistan’s brisk early run rate in the middle of the innings before Amin ensured a competitive total at the end.
The 28-year-old left-hander smacked his 21 off the first five balls in an over from Ish Sodhi before the New Zealand spinner claimed the wicket off his final delivery.
Haris Sohail chipped in with 20 off 12 balls while Aamer Yamin, replacing the injured Hasan Ali, faced six deliveries for his 15.
New Zealand struggled from the start of their reply to get near the required run rate of more than nine an over, and were in early trouble when Faheem Ashraf claimed Kane Williamson for nine.
Martin Guptill attempted to bully the bowlers but it was primarily a lone stand. When he was removed for 59 off 43 balls in the 13th over, the required run rate had shot up to 13.57.
Ross Taylor put the ball over the boundary fence three times in his 25 off 10 balls.
But with his dismissal in the 17th over, New Zealand were 128 for five and their hopes of a miraculous comeback were over.