Tim Southee became the third New Zealand bowler to capture 300 Test wickets as he claimed two Pakistan wickets to help push his side into a strong position at the close of play on the fourth day of the first match on Tuesday.
Pakistan were 3-71, still 302 runs from their victory target of 373, with Azhar Ali on 34 and Fawad Alam 21 not out.
They will need to bat the entire final day on a deteriorating Bay Oval pitch in Mount Maunganui on Wednesday to stop the hosts taking a 1-0 lead in the two-match series.
Southee joined Richard Hadlee (431) and Daniel Vettori (361) when he had Haris Sohail caught at short extra cover by Mitchell Santner for nine to reduce Pakistan to 37-3 after tea.
"I knew it was reasonably close," Southee told Spark Sport. "It's nice but we've still got a bit of work to do with the ball over the next day."
New Zealand captain Kane Williamson had declared his side's second innings at 5-180 about 30 minutes before tea after openers Tom Blundell and Tom Latham produced an 111-run first wicket partnership.
The pair survived a torrid opening spell from Shaheen Afridi and Mohammad Abbas, with several nicks falling short or wide of fielders, before Blundell brought up his second Test half-century in the first session.
Blundell was dismissed after the break for 64 as New Zealand looked to increase the tempo, with Latham falling for 53, his 20th Test half-century, before Williamson, Henry Nicholls and BJ Watling followed in quick succession.
Ross Taylor (12) and Santner (six) were left not out when Williamson called them in with a lead of 372 runs.
Trent Boult and Southee provided the best possible start when they dismissed Abid Ali and Shan Masood without a run being scored.
Meanwhile, New Zealand fast bowler Kyle Jamieson has been fined 25 per cent of his match fee for throwing the ball towards Pakistan batsman Faheem Ashraf "in an inappropriate and/or dangerous manner", the ICC said on Tuesday.
"The incident occurred ... on Monday, when Jamieson, after fielding the ball on his follow through, threw it in the direction of Faheem Ashraf at high speed when the batsman was away from the stumps but within the popping crease and not intending to take a run," the ICC said.
One demerit point was added to Jamieson's disciplinary record and it was his first offence in a 24-month period.