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.
Babar Azam's 107 off 117 balls propped up Pakistan's 334-6, and New Zealand stumbled to 232 all out, its lowest total of the series.
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.
Both teams will depart for Zimbabwe at the end of the series for their World Cup qualifying campaign which begins on June 18. The all-important tournament will confirm the remaining two spots for the 10-team ICC Cricket World Cup 2023, India.
Shami, India's pace spearhead, returned figures of 3-18 to help dismiss the Black Caps for 108 after the hosts elected to bowl first in Raipur.
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.
Kohli's third century in his last four matches and 116 by opener Shubman Gill powered India to 390-5 in Thiruvananthapuram, Kerala.