Henry Nicholls top-scored with 82, as New Zealand fought their way out of a hole to reach 280 for eight off their 50 overs after being sent in to bat.
After being reduced to 99 for six, Nicholls and Mitchell Santner, who scored 48, put on 79 runs for the seventh wicket. A quick-fire 48 not out from Matt Henry and a handy 31 from Mitchell McClenaghan - who had to leave a ball early after being hit in the face - gave New Zealand more valuable runs.
Mohammad Amir and Anwar Ali picked up three wickets apiece for Pakistan, with Ali dismissing key man Kane Williamson for 10, before claiming the scalp of Grant Elliott two balls later.
Giant opener Mohammad Irfan proved difficult too as he claimed two wickets, including the important one of Martin Guptill early.
After failing to score with the bat, Grant Elliott dismissed both openers and took three for 43 as New Zealand bowled Pakistan out for 210 in 46 overs.
Kane Williamson took the key wicket of Mohammad Hafeez in the 26th over, to break up Pakistan's best partnership of the match, which saw Hafeez put on 81 runs with Babar Azam.
Azam top-scored for Pakistan with 62, but found little support after losing Hafeez, with only Sarfraz Ahmed surpassing 20.
Trent Boult finished with handy figures of four for 40, although that came largely through cleaning up the tail.
Corey Anderson and Mitchell Santner also picked up wickets.
