Starting the day needing two wickets to take a 1-0 lead in the series, Pakistan, who are forced to host matches in the UAE due to security concerns back home, dismissed the visitors for 231 in the second innings on the fifth morning.
New Zealand leg-spinner Ish Sodhi (63) showed plenty of resilience to notch his second half century in Tests but was the last man to fall, out leg before to paceman Imran Khan.
Resuming on 174 for eight, New Zealand lost their penultimate wicket when leg-spinner Yasir Shah (3-74) bowled Mark Craig (28) in the second over of the day with a sharply turning delivery.
Sodhi, the highest scorer in New Zealand's second stint, added 54 runs with Trent Boult (19 not out) for the final wicket to delay Pakistan's celebrations.
Fresh from inflicting a 2-0 defeat on Australia, Pakistan have continued their dominance against New Zealand, all three wins coming without their two main strike bowlers -- banned off-spinner Saeed Ajmal and injured paceman Junaid Khan.
New Zealand captain Brendon McCullum was well aware of what was in store for the visitors in the remaining Tests, with the second match starting in Dubai on Monday.
"Obviously we were clearly second in this test match," McCullum said at the presentation ceremony.
"Spin is a threat but so is reverse swing. The partnerships at the end of our innings gives us confidence for the rest of the series.
"It would be nice if we could win the toss, bat first, and put some scoreboard pressure on Pakistan."
The victory against New Zealand also made Misbah-ul-Haq the most successful Pakistan captain with 15 wins, ahead of Javed Miandad and Imran Khan on 14.
The winning run has also helped the 40-year-old Misbah, who was panned for a lack of runs, silence his critics.
"It's a young team, nobody expected us to perform like this," a relieved Misbah said.
"Sometimes you have to be patient. It was an absolute disaster for me, I didn't get any runs in Sri Lanka and in the one-day series against Australia, but I kept calm through that."
Image: Pakistan captain Misbah-ul Haq (left) poses with Man of the Match Rahat Ali after beating New Zealand in the first Test at the Sheikh Zayed stadium in Abu Dhabi.
Photograph: Warren Little/Getty Images
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