Naseem dismissed opener Devon Conway for a first-over duck off a full-pitched delivery as the left-hander tried to flick the fast bowler but the ball ricocheted off his back leg onto his stumps.
Hard-hitting Finn Allen (29) successfully overturned a lbw decision against him in Haris Rauf’s first over. Allen hit Naseem for two boundaries in an over and smashed Rauf for three boundaries in a row before falling to a spectacular Agha Salman diving catch at short extra cover.
Mir tied down New Zealand through his googlies and sharp legspin, and stunned Kane Williamson on 26 off a turning delivery which knocked back the off stump.
Tom Latham (42) and Daryl Mitchell (36) rebuilt the innings with a half-century stand before falling to Mir and Nawaz respectively. New Zealand slipped to 147-5 in the 32nd over.
Michael Bracewell, who top-scored with 43 off 42 balls, and Glenn Phillips (37) also had good starts before Naseem returned and picked up four wickets in his return spell.
Naseem was on a hat trick after he clean bowled Bracewell and debutant Henry Shipley, but Tim Southee denied the pacer.
Mitchell Santner made a brisk 21 and Southee contributed 15 to get New Zealand past 250 runs.
Babar featured in two half-century stands with Zaman and Rizwan after offspinner Bracewell (2-44) dismissed Imam-ul-Haq (11) early in Pakistan’s chase.
Latham dropped a tough edge by Zaman before the left-hander’s 15th half-century. Zaman was clean bowled soon after while going for a slog sweep against Bracewell.
Babar also survived two close lbws against the spinners. Latham stumped him off part-time spinner Phillips.
Rizwan kept his cool and batted with cramps in the latter half of the run chase. Salman, 13 not out, hit the winning runs with a straight six against Southee.
Williamson said Pakistan were better adapting to the conditions.
“We would have liked a few more [runs]. Pakistan was very clinical with the ball in hand. Having said that it was competitive enough if we got things right in that second half and there was a lot of glimpses where the game could have changed quickly. There was assistance in both innings and the surface did change a bit, so there’s some learning there as well. They were very clinical and adapted to the conditions,
“A number of mid-partnerships but no one going on and building that big innings and giving us a good chance in those death overs. There was some good fight in that first half to get a competitive total but we want to be doing things a little bit better in all departments.”
The second ODI is on Wednesday followed by the last match on Friday.