Some hit and hope cricket in the last few overs carried Pakistan to a total which was only its second lowest in one-day internationals, matching its 74 against England in 1992.
Pakistan's bowlers seemed to get better as the ball got older, making excellent use of slower, shorter deliveries which confounded the batsmen when they didn't bounce or come onto the bat as expected.
Skipper Kane Williamson top-scored for the hosts with 73 runs off 101 balls while Ross Taylor finished with a well-paced 52 off 64.
Azhar Ali waas out for a second-ball duck from the final ball over the second over, bowled by Boult, and the left-armer took the next two wickets to fall as the Pakistanis fell to 3-2 in the fourth over.
Babar Azam (8), Shoaib Malik (3) and Shadab Khan (0) went in quick succession to leave Pakistan at 16-6.
While Man-of-the-Match Boult turned out to be the pick of the bowlers, Colin Munro and Lockie Ferguson contributed with two wickets apiece. "Tim and Trent to start off, just built up that pressure", he said. "I think everyone did their job in terms of the bowling performance and the most important performances were the ones from the far end". Such was his impact that at one point Pakistan was reeling at 7/17.
Taylor was able to score more freely than Williamson, perhaps because the conditions favored the straight-bat shots which are his forte, and reached his 40th ODI half-century from 49 balls.