Skipper Kane Williamson was batting on 27 and with him opener Jeet Raval on 26 not out as New Zealand still trail by 18 runs with nine second innings wickets intact.
Pakistan, resuming at 59-2, were dismissed for 227 in their first innings on the second day.
Babar Azam top-scored with 62 while Asad Shafiq (43) and Haris Sohail (38) were other contributors, helping Pakistan to a 72-run lead over New Zealand’s first innings total of 153.
Trent Boult finished with 4-54 while debutant spinner Ajaz Patel and medium pacer Coiln de Grandhomme took two wickets apiece.
The second Test is in Dubai (November 24-28) and third in Abu Dhabi (December 3-7).