Azhar was on 19 while Babar was 23 not out in Pakistan's second innings as they frustrated New Zealand's bowlers after Colin de Grandhomme had Sami Aslam caught behind for seven shortly after lunch at Hagley Oval in Christchurch.
Wagner, who returned figures of 3 for 34, claimed the wicket of Shafiq and Southee closed the innings when he had Rahat Ali caught for two.
The pair resume hostilities in Hamilton on Friday and captain Williamson has praised the way in which his seamers disposed of the tourists during the opening Test.
"Our bowling effort in the second innings", Williamson told reporters in Christchurch on Sunday as to what he had been most impressed by in the match. "The ball does it (moves around) for a couple of hours on the first day or two but it starts to settle down". This win would be welcome for the Blacks Caps after their loss to India 3-0 in the last Test series.
"It was important we learned a lot, but at the same time, put some of that baggage away and tried to focus on what we needed to do here".
"The first innings it did a bit for both teams and there were two low scores", Williamson told Sky sport.
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Former Pakistan opener Aamir Sohail has criticised the Pakistan Cricket Board (PCB) for its inability to find Test skipper Misbah-ul-Haq's successor, accusing the cricket body of "enjoying perks" and doing nothing so as to find the next captain. Though the appeal wasn't spontaneous, there was a sound as the ball passed the bat, but New Zealand couldn't refer the decision because they had no reviews left.
It took aggressive knocks in the 20s from de Grandhomme, Southee and Wagner to give the hosts a crucial 67-run lead.
Misbah has indicated in recent times that he was contemplating a retirement from all worldwide cricket. "He was very calm, very relaxed, and stuck to the game plan".
The match was weighted heavily in New Zealand's favor when Pakistan only managed to reach 129-7 at stumps on the third day, taking a slim 62-run lead.
"Colin's been a talented player for a long time but we've been waiting for something to click, to show he's worked out how to play at first-class level first".