The 22-year-old's first five-wicket haul in Test cricket helped New Zealand bowl out the tourists for 196 before the home side reached 75 for three wickets when stumps were drawn, a handsome lead of 245 runs.
The unbeaten batsmen were opener Mark Richardson on 35 and nightwatchman Darryl Tuffey, who had yet to score.
The Kiwis began their second innings after the tea interval but quickly lost Lou Vincent for four when he was adjudged lbw off the bowling of Shoaib Akhtar.
Danish Kaneria trapped Stephen Fleming in front for 24 before Shoaib had Richard Jones caught by wicketkeeper Moin Khan for seven in the penultimate over. The wicket was Shoaib's seventh of the match.
Butler finished with figures of six for 46 and was lethal with the new ball, taking five for 12 in five overs to remove Abdul Razzaq, Moahammad Sami, Shoaib, Moin and Kaneria.
Pakistan went to lunch on 134 for four and after a 56-run partnership between Yousuf Youhana and Razzaq the wickets began to tumble, with the last six batsmen falling for 28
Bowling into a northerly breeze, Butler's display was in stark contrast to his form in the drawn first Test in Hamilton, where he finished with two for 113 off 23.4 overs.
Youhana compiled a neat 60 before he gifted Fleming a slip catch off left-arm spinner Daniel Vettori, before Razzaq became Butler's second victim of the innings, clean bowled for 26.
Sami was next to go, caught behind by Robbie Hart, Shoaib was bowled for a three-ball duck, Moin was brilliantly caught in the covers by Vettori and Kaneria was trapped lbw to close out the innings.
Resuming on 52-2 in reply to New Zealand's 366, the star of the morning session was Jacob Oram who had a hand in both wickets to fall.
After scoring a Test best 97 to raise New Zealand's first innings total past the 300-mark and grabbing the wicket of opener Imran Farhat on Saturday, Oram caught Taufeeq Umar for 16 off Daryl Tuffey and trapped skipper Inzamam-ul-Haq leg before for 34.
