Mohammad Hafeez hit a solid 60, the 33rd ODI half-century for the veteran right-hander as he held the first half of the innings together.
Hasan then blasted his first 50 and Khan his second when they mounted a rescue mission with Pakistan 141 for seven in the 37th over.
The pair featured in a 70-run stand off 49 deliveries for the eighth wicket.
It was Sarfraz Ahmed's call to bat when he won the toss, saying it looked like a wicket that would favour the side having first use of it.
Imam-ul-Haq, in for the injured Fakhar Zaman, was out for two in the fourth over and Azhar Ali followed five balls later for six.
Lochie Ferguson reduced Pakistan to 39 for three when he entered the attack in the 11th over and immediately had Babar Azam (10) edging a ball to Ross Taylor at first slip.
Shoaib Malik, frustrated at being pinned down by Todd Astle, tried to hit the legspinner out of the park only to be caught at long on for 27.
Sarfraz Ahmed was stumped on three when he went down the wicket to Astle, and Hafeez lost his wicket dancing down the pitch to Mitchell Santner.
The left-arm spinner picked the move and sent down a short, wide delivery which Hafeez hit to Martin Guptill at short cover.
With Pakistan on the ropes, Shadab Khan and Hasan stepped up, cracking 21 off an Astle over as they upped the tempo.
Ferguson was the chief wicket-taker for New Zealand, with three for 39.
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