Mohammad Hafeez top scored with 81 as the tourists' batsmen finally managed to notch some runs, with Fakhar Zaman, Haris Sohail and captain Sarfraz Ahmed also posting half centuries.
Paceman Tim Southee led the New Zealand attack with three for 44 and skipper Kane Williamson took two for 32.
Pakistan finished their 50-over innings at 262 for eight, thanks to some big-hitting from Hafeez, who smashed 22 from the final over.
It was a gutsy fightback from a side that was reeling at 11 for two in the fifth over and looked in danger of another humiliation after being skittled for 74 in their last outing.
The gamble backfired when Faheem departed for one after edging a swinging Southee delivery to the wicketkeeper in the third over, bringing Babar Azam to the crease.
He lasted only nine balls before becoming Southee's second victim, trudging back to the pavilion with only three runs to his name.
Fakhar Zaman was lucky not to follow him on seven when he spooned the ball to mid-wicket, only for Colin Munro to drop the chance.
Haris, returning to the ODI arena for the first time since 2015, also failed to push on after reaching 50, smashing the ball to Henry Nicholls on the boundary as he looked for a big six.
Incoming batsman Shoaib Malik had an injury scare as he ran into the path of fielder Munro's throw while trying to scamper back to his crease and the ball hit him flush on the head.
Pakistan were 175 for five with 10 overs remaining before Sarfraz and partner Hafeez stepped up the pace.
Sarfraz Ahmed reached 51 off 46 balls while Hafeez's 81 included five fours and four sixes.
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