Pakistan has not hit Kiwis in one day's series since its victory in New Zealand 2011, which has lost 2014 (2-3 in UAE), 2015 (0-2 in New Zealand), 2016 (0-2 in New Zealand) and in January 2018 (0-5 in New Zealand).
Pakistan captain Sarfraz Ahmed said his team had been in a good position to force a win of the series.
"It's a kind of disappointing end," said Sarfraz. "But you can not fight nature, we found ourselves in a good position after a good total and then got a ladybug.
"We did not do well in the first game but overall we were the better side and if we had won this game there would have been icecream on the cake."
Pakistan had set a strong 279-8 after Sarfraz won the pitch and chose to swim and then their spearhead Shaheen Shah Afridi had dismissed Colin Munro for nothing in the first round.
When rain stopped playing, George Worker was undefeated at 18 and Henry Nicholls was 15 not out.
Pakistan batted well with Babar Azam, Fakhar Zaman and Haris Sohail all contributors before Lockie Ferguson took a career best 5-45 for 11 wickets in the series.
Zaman and Mohammad Hafeez (19) beat 64 for the first wicket before Hafeez threw a defense with his heel and worked Ferguson to the long leg, which led to Azam being smashed in the 14th quarter.
Zaman struck eight boundaries in his eighth and eighteenth century before being caught on the long border outside Colin de Grandhomme for 65 years.
Azam then paced the innings during a third wicket stand of 108 with Sohail.
Sohail hit two six and six boundaries in his 59-ball 60 before being caught in depth outside of Ferguson. Azam met 100 balls for his 92 but it was only four four and one six.
He finally fell in the 49th as he tried to reach his ninth one day a hundred, caught in the depths of Trent Boult, little comfort for the left leg, whose east east cost 80 runs.
Pakistan lost four wickets in the last two transitions and can regain points only 38 runs in the last five. Ferguson's former best of 3-17 came against the West Indies in Christchurch last December.
New Zealand was without his shipwreck Kane Williamson who was injured by Tom Latham, who led the side.
Pakistan broke out Imam-ul-Haq for caution after he hit a battle against his helmet in the second match on Friday.
The two teams now play a series of three tests, with the first to start in Abu Dhabi from Friday.