In the early minutes of the second half at Auckland's Eden Park, New Zealand forward Hannah Wilkinson scored in style in the box after quick teamwork.
In the second half, Norway's Tuva Hansen had an effort from distance to hit the woodwork but New Zealand goalkeeper Victoria Esson made a fingertip save.
Norway's Guro Reiten lost a chance in the box in injury time, as New Zealand took a historic win.
In their next fixture in Group A, New Zealand will face the Philippines on July 25 in Wellington.
On the same day, Norway will play Switzerland in Hamilton.
Before the kickoff, both New Zealand and Norway players, and the fans in the stadium have observed a minute of silence over the Auckland shooting that killed at least two people, and injured six others including a police officer.
The 2023 Women's World Cup will run through Aug. 20.
