Chasing a daunting 276-run target, Pakistan were bowled out for 207 in 43.3 overs with paceman Matt Henry returning career best figures of 5-30.
Haris Sohail top-scored with 65 while Ahmed Shehzad made 54.
New Zealand were lifted to 275-4 by skipper Kane Williamson who made 97 while Ross Taylor scored an unbeaten 88.
Pakistan won the first and third matches while New Zealand came back to level the series in second and fourth games.
The two sides had shared the preceding three-Test and two-Twenty20 series 1-1.
Since 2003 Pakistan have won only one of the 12 final matches after the series was tied at 1-1 or 2-2, with their only win coming against Zimbabwe in 2013.