Azam smashed 101 off 58 balls while bowler Haris Rauf claimed a second successive four-wicket haul as New Zealand's chase fell short of the 193-run target set by Pakistan.
"Definitely, I am very happy to perform in this match," said Azam. "I tried to stay till the end and play all overs and utilized the last few overs and we managed to get a good total.
"Our bowling line-up is excellent. We have got experienced bowlers and some exciting young bowlers."
Azam enjoyed a 99-run partnership with Mohammad Rizwan before the fall of the first wicket and although Fakhra Zaman, Saim Ayub and Imad Wasim were dismissed cheaply, Pakistan powered on once Iftikhar Ahmed came to the crease.
Mark Chapman shone for New Zealand with the bat, hitting 65 runs off 40 deliveries to remain unbeaten.
But it was the bowling of Rauf that again undid the tourists, the 29-year-old restricting New Zealand to 154 as he claimed his four wickets for 27 runs to surpass his performance in the previous night's win.
"We have been there or thereabouts but we weren't able to finish the innings off, both with the ball and bat," said Black Caps captain Tom Latham.
"When Babar plays like that, you tip your hat off. The bowlers are trying hard and we are not that far away.
"We were a lot better than last night. You need to get off to a quick start while chasing 190 and we weren't able to do that today."
