Pakistan lost Asad Shafiq in seamer Tim Southee's penultimate over for 44 to close the third day on 281-6, still trailing by 122 runs on New Zealand's first innings total of 403.
Sarfraz Ahmed was unbeaten on 28 and Yasir Shah on one in a day when the Pakistani batsmen failed to score big after getting good starts.
Leg-spinner Ish Sodhi led the New Zealand bowling with 2-65.
Trent Boult, who got the prized wicket of Pakistan captain Misbah-ul Haq, termed it a good day for New Zealand.
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Pakistan, resuming at 34-2 saw off the first session without losing any wicket as Younis Khan (72) and Azhar Ali (75) shared a 113-run stand for the third wicket.
But New Zealand got four wickets in the next two sessions to press home their claims for a useful lead and in turn improve their chances for a series-levelling win.
Pakistan won the first Test by 248 runs in Abu Dhabi.
Trent Boult claimed his first wicket in the series when he produced a beautiful delivery which got the edge of Misbah's bat and landed in the safe hands of Ross Taylor at first slip.
Misbah's 28 had two fours and a six.
Ali drove spinner Mark Craig through point for three to complete his 18th half-century.
But he too fell soon, trying to cut Sodhi and was bowled. He hit six boundaries and a six during his patient five-hour 22-minute vigil.
He too failed to bat for long and was caught off a loose shot in the end, adding 59 for the sixth wicket with Sarfraz.