Pakistan had needed two wickets after their opponents resumed at 174-8 but it took only 16.3 overs for them to reach their target as New Zealand folded at 231 in 70.3 overs.
Kiwi Mark Craig, who along with Ish Sodhi (63) had delayed Pakistan's defeat after batting for 14.5 overs on Wednesday, couldn't prolong his resistance as he was bowled by leg-spinner Yasir Shah for 28 off the first ball of the second over in the day.
Sodhi hit seven boundaries and a six during his two-hour resistance before he was finally trapped leg-before by paceman Imran Khan, who finished with 2-37.
Shah finished with 3-74, while Zulfiqar Babar and Rahat Ali took two wickets for 48 runs each.
This was Pakistan's third Test win in a row after they white-washed Australia 2-0 last week, their first series win over the Aussies for 20 years.
It was again a case of Trans-Tasman neighbours Australia and New Zealand failing to cope against Asian spinners.
But New Zealand still has a better record in the continent than their Aussie cousins, losing six of their 13 Tests, winning two and drawing five.
Australia have lost 10 of their 15 Tests in Asia, with only one win and four draws.
Babar had taken 14 wickets and Shah 12 in Pakistan's win over Australia and the same two bowlers also came good against New Zealand as well.
For Pakistan, Ahmed Shehzad hit a career best 176 and Younis Khan and Misbah smashing hundreds in the team's first innings total of 566-3 declared.
Tom Latham scored his maiden hundred for New Zealand in a paltry 262-run total in the first knock.
Mohammad Hafeez scored his first hundred since July 2012 in Pakistan's second innings.
The second Test starts in Dubai on November 17 while the third and final in Sharjah from November 26.
The two teams will also play two Twenty20 and five one-day internationals, also in United Arab Emirates.
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