MORE: Hafeez century puts Pakistan in strong position
Mohammad Hafeez was the star on Wednesday with his seventh Test century, the opener finishing the day 178 not out in Sharjah.
Azhar (39) contributed to an 87-run partnership with the opener, with captain Misbah-ul-Haq's 38 not out further strengthening Pakistan's position.
The 29-year-old believes they are now well set to build a big first-innings total on day two, knowing they must simply avoid defeat to wrap up the three-match series.
"We are very, very glad with the way we all batted," said Azhar. "I think it is very important when you win the toss and bat first, you make sure you make big runs on it.
"We have had a very good start now so we want to capitalise on it and hopefully tomorrow we continue that and the partnership just now that is going on, hopefully we will try and make a big score in the first innings.
"On a good track you want to make it big and bat as long as you can and make at least 500 on this wicket. So I think our target is at least 500 and anything over that will be very good for us."
One positive on a largely tough day for New Zealand was the wicket-taking return of Daniel Vettori (1-28), the veteran making his first Test appearance since July 2012, and fellow spinner Mark Craig (2-67) relished the chance to learn from the 35-year-old.
"[It's] awesome," said Craig. "He's got a wee bit of an aura about him, and it's nice to have him out in the field and play in a Test match with us.
"He's a quality player and all the boys love having him there."