A low-scoring match was wrapped up inside eight sessions after the first day's washout, with Williamson's second innings 61 -- his 24th Test 50 -- the top score of the match.
Set 105 to win after Pakistan were all out for 171 in their second innings on the morning of the fourth day, Williamson lost his wicket with the scores level, leaving debutant Jeet Raval to seal victory with a boundary off Yasir Shah.
"It was a nice toss to win," said Williamson who put Pakistan into bat on a seaming wicket and had them all out for 133 in their first innings.
"After a couple of really tough tours in South Africa and India, it was important we learned a lot but at the same time put some of that baggage away."
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Azhar Ali, who will take over the Pakistan captaincy with Misbah-ul-Haq having to dash home after the match because of a family illness, said the tourists had no excuses.
"As a professional, as a team, we have to adapt to conditions wherever we go," Azhar said.
"If you come to this part of the world, you expect that. You expect sub-continent teams will be tested with that short stuff and we all knew that.
- Debutants shine -
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"As time goes on, we'll get better. We're hopeful to turn things around quickly."
New Zealand's debutants shone. Opener Raval was unbeaten on 36 in the second innings after top-scoring in the first innings with 55 while Colin de Grandhomme gave a masterful display of medium-paced bowling, taking 6 for 41 in the first innings when Pakistan were skittled for 133.
Sohail Khan posted a Test-best 40 as he and Asad Shafiq (17) showed gritty resistance at the start of the day.
But their 53-run stand for the eighth wicket came to an end when Sohail half-heartedly pulled a short-pitched Southee delivery to de Grandhomme at backward square.