It took the Black Caps until the final over of a prolonged day's play to dismiss Pakistan, 192 runs short of the hosts' first innings total in the first Test in Mt Maunganui.
Chasing the Black Caps score of 431, Pakistan started day three 30-1 and were all out nearly eight and half hours later for 239.
Pakistan scored just 82 runs in the first two sessions of the day, and lost five wickets, to go to tea at 112-6, trailing New Zealand's first innings total by 319 runs.
Number 8 batsman Faheem Ashraf was the reason Pakistan avoided the follow-on.
Faheem made his highest score in Test match cricket but fell just short of a milestone century when he was the last man out on 91.
Pakistan's stand-in captain Mohammad Rizwan formed a big partnership with Faheem that saw both players pass the 50-run mark in the evening session.
Rizwan came to the crease with Pakistan 52-5 but he managed to survive where those ahead of him in the batting order could not.
Rain and hail interrupted play after lunch and the teams took an early tea only for more wet weather to further delay play, but once the action resumed Rizwan and Faheem dug in.
It took some sharp fielding from Mitchell Santner to run out Rizwan for 71 late in the day.
Kyle Jamieson's miserly bowling was a standout in a New Zealand attack that restricted Pakistan for long periods of time.
Jamieson made the first breakthrough of the day, in the 13th over of the morning to dislodge Abid Ali for 25 off 104 balls and he claimed Faheem's wicket to end the day's play.
Prior to the start of the day's play bowler Neil Wagner had an x-ray to determine the damage done when he was hit on the foot while batting on day two.
Wagner had broken his toe but was given clearance to play by the doctor if he could tolerate the pain and he did not hold back and finished the day with two wickets.
Tim Southee and Trent Boult could not be kept out the action, taking two wickets each.
Day four will start at the earlier time of 10.46am to make up for time lost on Monday.