Needing 251 for victory on the final day, Pakistan were dismissed for 218.
Umar Akmal backed up his 129 on debut by topscoring with 75 to become just the ninth test player to compile a century and half-century on debut.
Man-of-the-match Shane Bond, playing his first test for two years, led the New Zealand attack with figures of three for 46 from 21 overs and was well supported by Iain O'Brien, with three for 63, and Chris Martin, who took two for 45.
Fast bowler Bond had a match analysis of eight for 153.
The second test of the three-match series starts in Wellington on Thursday.