REACTION: Azhar eyes big first-innings total
The opener took his tally to 375 runs in his last three innings against the Kiwis with an unbeaten 178 in Sharjah, just 18 shy of his best total in Tests.
Hafeez suffered only a couple of notable scares in his 262-ball knock, missing a teasing Tim Southee (0-43) delivery and surviving a caught-behind appeal off Daniel Vettori (1-28).
He struck 23 fours and three sixes during his day at the crease, looking particularly strong in front of square on both sides of the pitch.
Pakistan captain Misbah-ul-Haq opted to bat having won the toss and saw Hafeez and Shan Masood (12) make a steady start.
The opening pair shared a 44-run stand before Mark Craig (2-67) removed Masood in the 17th over, the spinner expertly finding a gap between bat and pan.
Masood's dismissal brought Azhar Ali to the middle and his 87-run partnership with Hafeez lifted the hosts into three figures, the latter outscoring his team-mate by seven runs in a well-balanced pairing.
Two quick wickets, including Vettori's first since July 2012, saw the hosts slip to 160-3, but Hafeez and Misbah (38) steadied the ship until the close.
Azhar was first to go as he became Craig's second victim, edging to slip, while Vettori trapped the dangerous Younis Khan lbw for five.
Younis reviewed the decision, but the television umpire confirmed Paul Reiffel's decision and Vettori had his man.
New Zealand toiled in the field for the remaining 39 overs of the day without any joy as Misbah and Hafeez rotated the strike well and pounced on anything loose.
Misbah will have his sights set on a 27th Test half century on Thursday as he reached the close in good touch, while Hafeez has much bigger milestones ahead of him, with Pakistan simply needing to avoid defeat in order to wrap up the series.