Put in charge of the squad ahead of the T20 World Cup in June, Shaheen (23) claimed three wickets and promoted himself in the batting order but New Zealand still went 1-0 up in the five-match series.
Put into bat, New Zealand racked up 226-8 with Daryl Mitchell hitting 61 off 27 balls and skipper Kane Williamson making a brisk 57.
It was an eventful outing for Shaheen, who dismissed Devon Conway with the second ball of the match but bled 24 runs in his second over when Finn Allen smacked him for three fours and two sixes.
Shaheen returned to remove the dangerous-looking Mitchell and also dismissed Adam Milne to finish with expensive figures of 3-46.
Debutant Abbas Afridi, who claimed 3-34, was the pick of the Pakistan bowlers.
Babar Azam, who scored 57, anchored Pakistan's chase for a while but Tim Southee (4-25) led New Zealand's disciplined bowling, which was aided by their sharp catching, as they bowled out the visitors for 180 in 18 overs.
Shaheen promoted himself to number seven but the ploy did not work as he fell for a duck.
New Zealand spinner Mitch Santner sat out after testing positive for COVID-19, the team said.
Santner has been in isolation at the team's Auckland hotel and will travel solo home to Hamilton, which hosts the second match on Sunday.
