Haris Sohail scored an unbeaten 85 while Shahid Afridi made a 51-ball 61 with seven boundaries and a six as Pakistan chased down a 247-run target in 49.3 overs.
Ross Taylor hit an unbeaten 105 to anchor New Zealand to 246-7 in their 50 overs after paceman Mohammad Irfan had derailed them with 3-57.
Earlier, New Zealand batting first managed 246-7 in their 50 overs.
Ross Taylor top-scored with a fighting 105 not out while Daniel Vettori made 27 and Luke Ronchi got 23 after paceman Mohammad Irfan took 3-57.
The second match will be played in Sharjah on Friday.