His run out of Mohammad Rizwan reduced the hosts to 128-3 in the 25th over, but that brought together Azam and Agha Salman who responded with a 117-run stand.
Salman dominated the spinners with sweep shots as he hit 58 off 46 balls, before Henry removed him with a brilliant low one-handed catch off his own bowling.
Azam completed his century and became the quickest batsman to reach 5000 ODI runs, needing 97 innings to edge ahead of Hashim Amla (101).
The Pakistan skipper then holed out to give debutant quick Ben Lister his first ODI wicket, before Shaheen Shah Afridi and Mohammad Haris smashed 38 off the last two overs to set up an imposing target.
“The way [Azam] batted and constructed that innings, he was able to put us under pressure,” Henry said. “It was a good challenge for us, and I think we bowled well in periods, but Pakistan finished the innings off really strong.”
New Zealand were in a similar position to the hosts at the halfway stage of their chase, sitting on 129-3 after Daryl Mitchell’s dismissal in the 26th over.
Captain Tom Latham (60 off 76) and Mark Chapman (46 off 33) then tried to accelerate in the middle overs, but Latham’s demise triggered a collapse as the Black Caps lost their last seven wickets for 48 runs.
“We lost wickets at key times, and I suppose that was through the pressure that Pakistan were able to apply with the ball,” Henry said.
“They know these conditions very well and they know how to create pressure, and I think that’s probably been the difference in these games. The way Pakistan have played in their conditions, they’ve just been slightly ahead.”
The Black Caps will welcome back several reinforcements when they attempt to bridge that gap at the World Cup in India. And ahead of the final match of a tour that began with a 2-2 split in the T20 series, Henry said his teammates would be better for the experience.
“Coming here in different conditions, you want to test yourself against what is a really strong Pakistan side,” he said. “It’s a shame we haven’t had the success we wanted to, but we’ve grown in a lot of areas and have been able to give experience to a number of guys as well.
“Guys are learning, even though it’s never nice not to win.”
-with AP