Opener Martin Guptill raised his 13th ODi century, 12 innings since his previous ton against South Africa last March.
Pakistan slumped to 57 for five before Haris Sohail and Shadab Khan combined for a 105-run partnership that steadied the innings.
In the final ODI of the series, New Zealand captain Kane Williamson won the toss and chose to bat first, putting it down to playing on the same surface that the first ODI was played on.
Henry makes his first global appearance since the Boxing Day ODI against the West Indies, replacing world class left-armer Trent Boult, who is rested.
His wicket triggered a middle-order collapse as the New Zealanders lost 31-4, including three in the space of five runs after Taylor followed Guptill back to the pavilion.
He posted his 13th ODI century from 125 balls on Friday and was out one ball later for exactly 100 while Taylor completed his 41st one-day worldwide half century and went on to make 59 before falling in the 45th over.
Guptill got off the mark spectacularly, a trademark straight drive off Aamer Yamin clearing the sightscreen, and Colin Munro (34 off 24) looked like he'd go large before trying one big shot too many. But then Colin de Grandhomme really took over Pakistani bowling and snatched the victory with his blistering 74 runs off just 40 balls.
But the tail wagged as Faheem Ashraf (23), Aamer Yamin (32) and Mohammad Nawaz (23) all made late cameos that left the tourists on nine for 249 and needing 23 off the final two overs.
For Pakistan, pacer Rumman Raees was the pick of the bowlers as he claimed three, whereas all-rounder Fahim Ashraf claimed two wickets.