Openers Brendon McCullum and Tom Latham resisted seven overs to get to stumps.
Earlier, New Zealand's bowlers persevered but the fielders let them down with dropped catches.
There was brief respite in the middle session when Ish Sodhi produced a candidate for 'best ball bowled by a New Zealand leg spinner' to clip the top of Azhar's off stump.
That 'reduced' Pakistan to 373 for three which offered cold comfort as Misbah strode to the wicket.
The run fest could have been stymied, slightly. In the 138th over, with Pakistan 422 for three, Sodhi coaxed Misbah into a slog sweep, only for the ball to sky in front of point.
Mark Craig hesitated and eventually grasped air. The following Sodhi over, Jimmy Neesham splattered a regulation catch at cover, as Misbah teed off again.
There can't be anything more demoralising for a bowler like Sodhi, on the cusp of cracking the highest level of the game, when he's so reliant on others' hands to secure his future. One for 162 off 43 overs looks grim, yet he was the most potent bowler. He remains the country's best bowling hope in this test and for the next decade on the sub-continent. New Zealand can't afford for him to be disheartened.
"It was hard to watch those go down," said Trent Boult. "We'd worked hard to stick at them and not let them have anything.
"Their batsmen showed patience and really didn't give us much. They know these conditions well, so good on them."
"A couple of days in the dirt tends to do that," said Corey Anderson, reflecting on the spills. "They were little slips in concentration."
Anderson produced venom before lunch, dismissing Ahmed Shehzad hit-wicket. The opener shaped to pull but missed; his right temple took the brunt. His bat hit the stumps as he hit the ground. The New Zealanders celebrated while Shehzad writhed in mental and physical agony. He was subsequently taken to hospital for a scan; the diagnosis was a minor fracture to the skull.
Shehzad became the 12th player and fourth Pakistani to have been dismissed 'hit wicket' by New Zealand in test history.
Misbah-ul-Haq and Younis Khan added 193 for the fourth wicket. Photo / Getty Images
Last five innings:
Misbah-ul-Haq - 3, 69, 101, 101*, 102
Younis Khan - 106, 103, 213, 46, 100
Scoreboards can be deceptive. The New Zealand bowlers - and there are six recognised experts in this XI - didn't do much wrong. A run rate of 3.31 was testament to that.
Tim Southee and Boult again pitched up to make the most of the new ball, dropped in the odd calculated short one, and tested their opponents around the wicket. Like Sodhi, Craig also offered flight but the batsmen were so assured there was barely a chance to test the vocal chords for an lbw, or even achieve a moral victory with a one-hand, one-bounce.
The first and only review for an unsuccessful lbw came in the 159th over when Pakistan were 508 for three.
McCullum rolled his captain's dice with the fielding positions. He had two short mid-wickets and a silly mid-off for Boult; vice-versa for Southee plus a straight silly mid-on; and a leg slip, short leg and short mid-wicket for Craig's off-spin. Nothing doing.
"I don't think I've seen a wicket that flat," Boult said. "The ball was a mess. It swung early but got chewed up so quickly.
"I'm not sure if 'punishing' is the right word but it was an extremely hard couple of days' toil. Them pushing through to 566 for three is tough to stomach but one positive is we're 15 without loss.
"We've got a good track to bat on if we can get close to them."
However, the pitch is due to decay.
New Zealand needs a comparable first innings total before placing faith in Sodhi and Craig to gain second innings traction.
- Andrew Alderson travelled to the UAE courtesy of Emirates
