Pakistan, who won the first match of the series in Abu Dhabi by 248 runs, were all out for 259 in their second innings in Sharjah on Sunday (local time).
Asad Shafiq staged a lone battle for Pakistan and completed his fifth test hundred with an aggressive 137 off 148 balls but ran out of partners in the end.
On a docile pitch at the Sharjah Cricket Stadium where New Zealand posted their highest total in tests, the 25-year-old Boult extracted enough movement and pace to rattle the Pakistan top order.
Shan Masood (4) edged Boult to Tim Southee at slip in the third over, while the paceman bowled Azhar Ali (6) with the last delivery of his fourth over and then returned to dismiss Younus Khan for a duck leg before with the first ball of his next.
Off-spinner Mark Craig, who took seven wickets in the first innings, continued to punish Pakistan by dismissing opener Mohammad Hafeez and captain Misbah-ul-Haq.
Hafeez (24) looked solid before he fell in the second over after lunch, offering a tame return catch to the 27-year-old Craig. Misbah (12) then reviewed the umpire's bat-pad decision off the same bowler but failed to overturn it.
Sarfraz Ahmed (37) took the attack to the New Zealand bowlers and added a quickfire 73 for the sixth wicket with Shafiq.
But leg-spinner Ish Sodhi, who saw Sarfraz dropped twice off his bowling in one over, took out the wicketkeeper-batsman and Yasir Shah (10) to take New Zealand closer to victory.
The 28-year-old Shafiq smashed 18 fours and six sixes in his knock and added 78 for the ninth wicket with Rahat Ali to delay New Zealand's celebration. He fell to Boult.
Rahat became the last man out and Craig's 10th victim in the match.
Earlier in the morning, New Zealand's first innings closed on 690 with Craig (65) becoming the sixth batsman to score at least a half-century in the innings.
The visitors hit 22 sixes in total, another record for the most number of maximums in a test innings.
Paceman Rahat and leg-spinner Yasir Shah picked up four wickets each for Pakistan, while part-time off-spinner Hafeez, who was reported for an illegal action after the first test in Abu Dhabi, took the remaining two wickets.
