A century from Ross Taylor means Pakistan have a hefty mountain to climb if they want to square the Test series with New Zealand.
Taylor struck 102 not out late on the fourth day in Hamilton and New Zealand declared at 5-313 just before stumps, leaving Pakistan a target of 369 for victory.
Openers Sami Aslam (1) and Azhar Ali (0) safely negotiated the day's final three overs.
Taylor's 16th Test ton belied problems with his left eye - where a pterygium growth will be cut out following the match - and he struck 16 fours during the largely untroubled innings.
Other contributions came from Tom Latham (80), Kane Williamson (42) and Colin de Grandhomme (32).
Latham and Williamson shared a partnership of 96 runs and Taylor shared half-century partnerships with Latham, Watling and Henry Nicholls.
New Zealand had started the final session at 3-181, a lead of 236, and were able to accelerate throughout the session.
Nicholls was disgusted with himself when he chased a very wide ball from Imran Khan and could only get a faint edge through to the keeper, to be out for 26.
The Canterbury left-hander had struggled to get his innings started but was starting to get his eye in when he paid the price for chasing an ugly wide one.
An aggressive de Grandhomme then helped take the lead past 300 in hitting six fours before he skied an attempted pull off Imran Khan and was caught at mid off.
The highest fourth innings total at Seddon Park was the ground's first Test when Sri Lanka scored 6-344 in the drawn match in 1990-91.
The highest successful fourth innings chase at the ground was Australia's 4-212 in 2000.
Leading the two-match series 1-0, the Kiwis need at least a draw to secure their first series win over Pakistan since 1985.
Pakistan are also trying to preserve a seven-series unbeaten streak that goes back to 2014.
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