The Black Caps won the last match of the five-match T20I series by six wickets at the Pindi Stadium Monday.
Pakistan posted a target of 194 runs as New Zeeland opted to bowl after winning the toss.
Mark Chapman's blitz secured the victory for Black Caps.
Mohammad Rizwan missed a century by two runs but still guided Pakistan to a solid 193-5.
The visitors achieved the 194-run target to win their crucial Twenty20 match to level the series.
Mohammad Rizwan struck 62-ball unbeaten 98 as he missed the last delivery of the innings and his second hundred after New Zealand sent Pakistan in to bat.
Rizwan, who struck four sixes and seven fours, added 71 for the fourth wicket with Iftikhar Ahmed (36) and another 68 for the fifth with Imad Wasim who made 31.
For New Zealand pacer Blair Tickner was the best bowler with 3-33.
PLAYING XIs
New Zealand: Finn Allen, Devon Conway (wk), Kane Williamson (c), Glenn Phillips, Daryl Mitchell, James Neesham, Mitchell Santner, Tim Southee, Ish Sodhi, Lockie Ferguson, Trent Boult
Pakistan: Babar Azam (c), Mohammad Rizwan (wk), Mohammad Haris, Fakhar Zaman, Shan Masood, Iftikhar Ahmed, Mohammad Nawaz, Shadab Khan, Mohammad Wasim Jr, Naseem Shah, Shaheen Shah Afridi, Haris Rau