Hafeez was on 123 for his seventh Test hundred and with him skipper Misbah-ul Haq four not out after Pakistan won a crucial toss and decided to bat on a flat, grass-less Sharjah stadium pitch.
New Zealand, seeking to level the three-match series after losing the first in Abu Dhabi by 248 runs and drawing the second in Dubai, hit back in the second session by dismissing Azhar Ali (39) and in-form Younis Khan for five.
Ali added 87 for the second wicket with Hafeez.
Younis, who hit three hundreds in Pakistan's 2-0 rout of Australia last month and one more in the first Test of this series, was trapped leg-before by left-arm spinner Daniel Vettori.
Vettori, recalled in place of Jimmy Neehsam, is playing his 112th match for New Zealand, becoming his country's most capped player beating Stephen Fleming who played 111.
Vettori also played one Test for an ICC World XI in 2005.
He has so far hit 17 boundaries and two sixes during his dominating 158-ball knock.
In the first session, Pakistan had a confident start of 44 before Craig bowled Shan Masood for 12.
Pakistan made two changes from the Dubai Test line-up, dropping out-of-form opener Taufeeq Umar and Ehsan Adil, who suffered a side-muscle strain. They brought in Hafeez and paceman Mohammad Talha.
New Zealand entered the Test with three spinners after recalling Vettori, playing his first Test for 28 months.
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