Pakistan were dismissed for 259 in their second innings, despite an aggressive 137 off 148 balls from Asad Shafiq, who ran out of partners after paceman Boult (4-38) ripped through the top order.
Mark Craig chipped in with 65 runs as New Zealand posted 690 all out, their highest total in Tests, leaving Pakistan with a mountain to climb in their bid to avoid defeat.
They made a dismal start, losing Shan Masood (4) quickly when he 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.
Boult then returned to dismiss Younus Khan for a duck, trapping him leg before with the first ball of his next over.
Off-spinner Craig, who took seven wickets in the first innings, continued to punish Pakistan by dismissing opener Mohammad Hafeez (24) and captain Misbah-ul-Haq (12).
Sarfraz Ahmed (37) finally offered some resistance, adding 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, eventually snared the wicketkeeper-batsman and Yasir Shah (10) to edge New Zealand closer to victory.
Shafiq smashed 18 fours and six sixes in his knock, adding 78 for the ninth wicket with Rahat Ali to delay the inevitable.
But Craig would complete the win with the wicket of Rahat as New Zealand ended the final match on a high after a heavy 248-run defeat in the opening encounter.