Anwar Ali also took three wickets and Mohamhad Irfan claimed two as Pakistan dominated New Zealand's top order.Amir, whose three wickets were all caught behind, was struck on the foot by a Mitchell Santner drive and was forced from the field after bowling 8.1 overs.
Young batsman Henry Nicholls, a late replacement for injured Ross Taylor, led New Zealand's rally with a spirited innings of 82.
He put on 79 for the seventh wicket with Santner (48) to turn the tide of the match, then Matt Henry made a career-best 48 not out in a late-innings slog with Mitchell McClenaghan (31).
The late assault took off in the 46th over, bowled by Wahab Riaz, from which Henry hit two sixes and McClenaghan one. Henry went on to hit four sixes and four fours and McClenaghan two sixes and three four before being felled by a bouncer from Anwar on the second-to-last ball of the innings.
The ball passed through a gap in McClenaghan's visor, striking him in the left eye and forcing him to retire hurt. No. 11 Trent Boult came out to face the last ball of the innings, from which he hit a boundary.
Amir resumed his international career on this tour after completing a five-year ban for his involvement in spot fixing.
He performed moderately during the three-match Twenty20 series, but on Monday he looked more the bowler he had been as an 18-year-old, when he became the youngest bowler to reach 50 test wickets.
Amir had the invidious task in his opening spell of bowling into the buffeting breeze at the Basin Reserve and played a support role as the 2.15 meter (7'1") Irfan softened New Zealand up with a hostile beginning.
But Amir found his rhythm in his later spell, striking an effective line and bowling with good pace. He took the early wicket of opener Tom Latham (11), then came back with a double breakthrough, dismissing Corey Anderson (10) and Luke Ronchi (5) in quick succession to leave New Zealand struggling at 99-6.
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