Haris Sohail and Azhar Ali, the overnight batsmen, added 32 more runs for the third wicket to keep New Zealand at bay for the larger part of the first hour.
Haris Sohail fell to a full toss from Ish Sodhi minutes before the drinks break in the first session.
Azhar Ali, dropped on 9 off Boult, fell to the same bowler when he edged one behind. New Zealand lost two wickets in a two overs as a result.
An 83-run stand between Asad Shafiq and Babar Azam ended with a thunderbolt from Boult that accounted for Shafiq.
Ajaz Patel, in the middle of an extended 11-over spell, struck in the next over to get rid of Sarfraz Ahmed. He also got Bilal Asif stumped.
Babar Azam scored 62 as Pakistan took a 74-run lead over New Zealand.
Hasan Ali bowled Tom Latham with his first delivery in the third innings, and a lot rests on Jeet Raval and Kane Williamson going into Day 3