A tight series had seen Pakistan twice take the lead, but the tourists came fighting back to make it 2-2 with a seven-run win in the fourth match on Wednesday.
With the Cricket World Cup on the horizon, both teams knew the importance of building momentum, and it was the Black Caps who came out on top in the Abu Dhabi decider on Friday.
Captain Kane Williamson made his eighth 50-plus total in 10 ODI innings as he posted 97, while Ross Taylor hit an unbeaten 88 - New Zealand setting a target of 276.
Nasir Jamshed's dismissal for a duck at the hands of the impressive Henry (5-30) in the opening over of the Pakistan innings got their chase off to a far-from-ideal start, and the designated hosts fell well short despite creditable contributions from Haris Sohail (65) and Ahmed Shehzad (54).
New Zealand elected to bat after winning the toss, but opener Martin Guptill was unable to lead by example - caught off a Mohammad Irfan (2-62) delivery in the third over.
Dean Brownlie's (34) partnership with Williamson lasted considerably longer after the latter stepped up to the crease in place of Guptill, but it was Williamson's work with Taylor that reaped most rewards as the pair made a 116-run stand.
New Zealand added a further 34 runs after Williamson had been caught behind, and things looked promising when Henry trapped Jamshed lbw.
Shehzad did his best to inspire Pakistan with a half century, but the wickets continued to fall, with Henry accounting for both the opener and Younis Khan (12).
Only three Pakistan batsmen managed to make it past 20 on a difficult day at the crease, and Sohail's 65 offered a rare glimmer of hope.
Wicketkeeper Sarfraz Ahmed (26) got a taste of his own medicine when he was caught behind by Luke Ronchi off a Henry delivery as he looked to build a decent score, before Henry completed his haul with the dismissal of Shahid Afridi (13).
The match would last just four more balls after Afridi's return to the pavilion, with Adam Milne (1-30) unsettling Zulfiqar Babar's (2) bails to seal the win with six overs to spare.