Debutant William Somerville took 3-52 to end up with a match haul of seven wickets. Fellow spinner Ajaz Patel finished with 3-42 while paceman Tim Southee also claimed three victims.
Earlier, Henry Nicholls scored his third test century, finishing with an unbeaten 126, as New Zealand declared their second innings at 353-7.
New Zealand won the opening test in Abu Dhabi by four runs before Pakistan squared the three-match series with victory in the second test in Dubai by an innings and 16 runs. (Reporting by Shrivathsa Sridhar in Bengaluru Editing by Toby Davis)
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