The Blackcaps have dismissed Pakistan for 156 in their second innings to seal a 123-run victory and a 2-1 series triumph on day five of the third and final test in Abu Dhabi.
Set 280 for victory on Friday, Pakistan suffered two separate batting collapses as New Zealand's bowlers secured a memorable victory - and their first away series against Pakistan in 49 years.
Debutant William Somerville took 3/52 to end up with a match haul of seven wickets. Fellow spinner Ajaz Patel finished with 3/42, while paceman Tim Southee also claimed three victims at the Sheikh Zayed Stadium.
"It was fantastic. Beating Pakistan in their backyard is very tough. It feels special, and this will be one that the guys remember for a long time," Kiwi skipper Kane Williamson said.
"We know the game can ebb and flow very quickly but we came out and played well today. The spinners that came along in this tour ... they played a huge part in our win."
Earlier, Henry Nicholls scored his third test ton, finishing with an unbeaten 126, as the Blackcaps declared their second innings at 353/7.
Williamson, who batted through the day on Thursday to score 139, was given out leg before wicket to seam bowler Hasan Ali with the first ball of the morning, leaving the visitors on 5/272.
Nicholls, whose 266-ball knock included 12 boundaries, then helped raise the scoring rate along with Colin de Grandhomme (26) as New Zealand scored 81 runs in nine overs.
Pakistan's reply began on a shaky note, as struggling opener Mohammad Hafeez was dropped by Williamson at second slip off paceman Tim Southee.
The 38-year-old was then bowled by Southee in the sixth over for eight. First innings centurion Azhar Ali perished for five, edging one to wicketkeeper BJ Watling off Colin de Grandhomme.
Somerville, who claimed 4/75 in the first innings, struck twice in two balls to remove Haris Sohail and the in-form Asad Shafiq to heap the pressure on Sarfraz Ahmed's side.
Babar Azam tried to steady the ship with a fighting half-century, but the Kiwis ran through the Pakistan tail to secure victory.
"If you look at the series, it was in our hands and we let it slip. We had our opportunities. Unfortunately our lower order couldn't score runs," skipper Ahmed said.
New Zealand won the opening test in Abu Dhabi by four runs before Pakistan squared the three-match series with victory in the second test in Dubai by an innings and 16 runs.