The 28-year-old smashed a 57-ball 104 in a rearguard action to lift New Zealand from a precarious 73-4 to chase down a stiff target of 194 with four balls to spare.
The final match of the series marks Pakistan skipper Babar Azam's 100th ODI in a glorious career which began in 2015.
Despite that and defeat in the final match on Sunday, Azam was in buoyant mood. "Winning the series is great and so is achieving number one ranking that has set us in a good position for the World Cup," said the skipper.
The 28-year-old crosses his milestone in just 97 innings, and breaks S.Africa Hashim Amla's record of 101 innings. Babar also becomes 14th Pakistani to score 5,000 runs in ODI cricket, with ex-captain Inzamam at the top of the list with 11,701 runs.
Pakistan, who won the first two matches by five and seven wickets respectively in Rawalpindi, took an unassailable 3-0 lead in the five-match series.
Zaman lifted Pakistan from 21-2 during a third-wicket stand of 154 off 161 balls with Mohammad Rizwan, who made a polished 74-ball 77 with six boundaries.
Azam's team won eight of the nine one-day internationals last year, including a 2-1 series win over a formidable Australia at home.
Naseem snapped up 5-57 as New Zealand was made to bat first and was restricted to 255-9. Rizwan, who was rested for the preceding drawn two-test series, top scored with an unbeaten 77 off 86 balls and eased Pakistan to 258-4 in 48.1 overs.
New Zealand's spinners strangled Pakistan on a turning wicket to win the second ODI by 79 runs Wednesday and level the three-match series 1-1.