While Pakistan made a bold effort to chase down New Zealand's 8-264 on Saturday, they fell short again and were dismissed for 221 in a match reduced to 42 overs per side due to a wet outfield.
New Zealand fast bowler Ben Sears took 5-34, his second five-wicket haul in consecutive matches.
Pakistan made a strong start to their chase despite a shocking injury to opener Imam-ul-Haq, who retired hurt in the third over after being struck in the head by a throw at the stumps.
Imam was attempting a quick single when a throw to the non-striker's end lodged in the grill of his helmet. He was clearly dazed and struggled to stand steadily before being helped from the field.
Babar Azam rallied Pakistan after the incident with a half century which, with support from Abdullah Safique (33) and Mohammad Rizwan (37), helped Pakistan to 1-95 at the midpoint of their innings.
With 10 overs remaining, Pakistan were 4-167 and well in the match with New Zealand 4-165 at the same stage in their innings. But New Zealand took 99 runs from the last 10 overs in their knock and Pakistan couldn't match that finish.
Tayyab Tahir made 33 from 31 balls but when he holed out in the 39th over with Pakistan 9-218, the chase was all but over.
Pakistan arrived in New Zealand with a new-look squad, eager to shrug off a disappointing performance at the recent Champions Trophy which they hosted and were hoping to build towards next year's T20 World Cup.
But the tourists lost the five-match T20 series 4-1 and lost the first two matches of the three-match ODI series by 73 and 84 runs respectively before Saturday's defeat. The Pakistan batters mostly struggled on fast and bouncy New Zealand pitches.
"Obviously it was a disappointing series for us," Pakistan captain Mohammad Rizwan said. "But if you look at the positives, Babar Azam is in very good touch. Looking at the bowling Sufiyan Muqeem was the guy.
"You have to give credit to New Zealand in all departments. They played very well for the last couple of months. They played well in Pakistan against us and they are true professionals."
Earlier, opener Rhys Mariu and Michael Bracewell made half centuries and Daryl Mitchell passed 2,000 runs in ODIs as New Zealand batted first after losing the toss.
Mariu posted his maiden half century in his second ODI and went on to make 58 from 61 balls. Mitchell came into the match with 1,998 runs in one-day internationals and finished with 2,041 runs from 52 matches in which he averages 49.7.
Captain Bracewell finished strongly, making 59 from 40 balls.
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