Boult first bowled danger man Fakhar Zaman off his pads, before Babar Azam nicked through to slip and Mohammad Hafeez was trapped in-front, with the home side in a funk at 3/8.
Earlier, in the first innings, Ross Taylor and Tom Latham scored fighting half centuries to lift New Zealand to a challenging total of 266 with nine wickets lost. It wasn't a demolition job by no means, just accomplished batting, calmly finding the gaps without too much risk.
In response Pakistan crumbled to 85-6, before Sarfraz Ahmed (64) and Imad Wasim (50) added 103 for the seventh wicket.
Only Danny Morrison and Shane Bond had previously taken hat-tricks in the one-day format for the Kiwis.
Ross Taylor has enraged Pakistan after levelling a stunning accusation at Mohammed Hafeez as New Zealand won their ODI clash on Wednesday.
Paceman Shaheen Shah Afridi, playing only his fourth one-day global, had jolted New Zealand at the start with the wickets of George Worker (one) and Colin Munro (29).
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Shadab dismissed Kane Williamson for 27 before Taylor and Latham joined at 78-3.
But once the Taylor-Latham fourth-wicket stand of 130 was broken, Pakistan's leg-spinner Shadab Khan derailed the innings with a burst of three wickets in the 42nd over to leave New Zealand at 210-7.
He dismissed Latham leg-before and did the same to Henry Nicholls (nought) the very next ball, before removing De Grandhomme two balls later when he edged to first slip without scoring. Boult also smashed a maximum off the last ball by Junaid Khan as Pakistan conceded 50 runs off the final five overs in an innings full of ebb and flow.
"A key part of the game is if you can get the ball moving around a little bit, and we all know what early wickets do to chasing totals", he told Sky Sport.
The victory gave New Zealand a 1-0 lead in the three-match series and extended their ODI winning streak against Pakistan to 12 matches dating back to December 2014.