Both Southee and Wagner ripped through Pakistan's batting line-up to leave the visitors in tatters at 76 for 5 at stumps, still 195 runs short of hosts' first innings total of 271.
Southee scalped three wickets while Wagner took two to leave the Azhar Ali-led side at sixes and sevens. Sami Aslam (5), Ali (1) and Younis Khan (2) were Southee's victims, while Wagner dislodged Mohammad Rizwan (0) and Asad Shafiq (23) at the fag end of the day.
Earlier resuming the day at 77 for 2, the Black Caps slipped to 119 for 5 before their lower order hauled them to 271.
BJ Watling showed tremendous composure to score unbeaten 49 to propel the home team to a relative position of strength.
He shared crucial partnerships of 33 and 36 with Mitchell Santner (16) and Southee (29), respectively.
Pakistan would be eager to come with a better performance in the remaining three days of the Test match to win the game and square the two-match series. The Black Caps are had won the first Test comfortably by eight wickets in Christchurch.
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