Seamer Trent Boult took 4-38 and Mark Craig 3-109 which overshadowed Asad Shafiq's career best 137 as Pakistan were dismissed for 259 in their second innings in the fading light at Sharjah stadium.
The win was more praiseworthy in a week when New Zealand were left grieved by Australian batsman Phillip Hughes's tragic death on Thursday, the day when both teams abandoned second day's play.
Boult ended Shafiq's fighting 183-minute knock of 18 fours and six sixes -- his fifth Test century -- with a short delivery.
He took 7-94 in the first innings.
Also Read
Boult struck thrice in the space of 18 balls to leave Pakistan struggling at 24-3 before Craig and Sodhi (2-82) chipped in.
Pakistan won the first Test in Abu Dhabi by 248 runs while the second ended in a draw in Dubai.
Pakistan's batting failure was miserable on a pitch where New Zealand plundered 690.
Shafiq and Sarfraz Ahmed (37) tried to take the attack to the New Zealand bowlers with a 73-run stand for the sixth wicket before Sodhi removed Ahmed and Yasir Shah (ten) in the same over before tea.
Hafeez gave a return catch to Craig while Misbah was adjudged caught behind off the glove on the same bowler and even a referral couldn't save the Pakistan skipper.
Earlier, Boult had shaken Pakistan at the start of the innings, dismissing Shan Masood (four) in his second over, bowled Azhar Ali (six) in his fourth and trapped Younis Khan for a first ball duck in his fifth in a destructive spell.
That gave New Zealand a huge 339-run lead over Pakistan's first innings total of 351 and they pressed home their advantage quickly with Boult's strikes.