Hafeez drove uppishly off a slower one from allrounder Corey Anderson who leapt in the air to hold onto a high catch for New Zealand's first wicket after toiling hard on a flat pitch at Abu Dhabi's Sheikh Zayed Stadium.
At the break, Ahmed Shehzad was just eleven runs away from his third hundred while Azhar Ali was on eight after Pakistan won the toss and opted to bat.
Hafeez and Shehzad had cut loose after Pakistan were 85-0 at lunch.
Hafeez though failed to reach his sixth hundred. He hit ten boundaries during his 212-minute stay at the crease.
More From This Section
The Hafeez-Shehzad stand was the best against New Zealand beating the 172 between Ramiz Raja and Shoaib Mohammad in the Karachi Test in 1990.
Shehzad has so far hit 11 boundaries off 196-balls.
New Zealand were unlucky in the first session as they missed two good chances.
Off-spinner Mark Craig almost succeeded but wicket-keeper B.J. Watling missed a stumping chance with Shehzad yards out of his crease after his forward push failed to connect. He was on 16 at the time.
Pakistan kept the same side which won the second Test against Australia by 356 runs in Abu Dhabi to secure a 2-0 series victory.
New Zealand entered the Test with two seamers and as many spinners.
The remaining Tests will be played in Dubai (November 17-21) and Sharjah (November 26-30).