Tim Southee snared his 300th Test wicket while Trent Boult also inflicted damage on Pakistan's top-order to leave the tourists reeling at 71 for three at stumps on the fourth day of the series opener.
New Zealand declared their second innings at 180/5 to set a gigantic target of 373 for Pakistan, who will be ramping up their defensive strokeplay to earn a draw.
Azhar Ali and Fawad Alam were the two unbeaten batsmen at the close of play. New Zealand require seven more wickets to claim an unassailable lead in the two-match series.
Pakistan's cause in their second innings was disrupted by the wizardry of Southee and new-ball partner Boult as the duo removed both openers for ducks.
Contrastingly, Pakistan's quick bowlers suffered from a lack of consistency as they were unable to get any assistance from the pitch. On the other hand, Southee and Boult had the opposing batsmen cowering to resist the masterful display of swing bowling.
Abid Ali tamely fended a rising delivery from Boult before Shan Masood was dismissed by Southee as his edge was safely grasped at first slip.
Azhar and Haris Sohail briefly dead-batted for 15 overs and just 37 runs for the third wicket, however, Southee soon sprang into action.
He got Sohail, whose feet were glued to the crease, to chip a rather innocuous delivery to Mitchell Santner at short cover.
The wicket enabled Southee to become only the third bowler from his nation to register 300 Test scalps. He joins the elite list headed by Richard Hadlee and Daniel Vettori.
Apart from Southee and Boult, Neil Wagner showcased his gritty character by delivering six overs with two broken toes.
New Zealand began the day's proceedings 192 runs ahead of Pakistan as Tom Latham and Tom Blundell extended the hosts' firm grip on the match by putting on 98 in the morning session.
Post-lunch, New Zealand discarded their conservative approach to focus on blasting regular boundaries, which increased the chances of soft dismissals.
Blundell was bowled for 64 when aiming for a wild slog off Mohammad Abbas and Latham fell for 53 when he mistimed a pull shot.
Naseem Shah was the most prolific bowler for Pakistan in his side's tepid bowling performance as his rapid bouncer barrage accounted for the wickets of Kane Williamson, Henry Nicholls and Latham.
Yasir Shah was uncharacteristically ineffective on the fourth-day pitch, darting in six uneventful overs.