It was the country's first-ever win at the World Cup and came in front of more than 42,000 in Auckland, the biggest crowd in New Zealand football history.
It capped a day which started when New Zealand's largest city was shaken in the morning by a shooting which left two victims and the gunman dead, the incident happening in a downtown area close to where several World Cup teams, including Norway, are staying.
The country's prime minister, Chris Hipkins, attended the match alongside FIFA president Gianni Infantino at Eden Park, where a moment's silence was held in memory of those killed.
The Football Ferns, who are co-hosting the first 32-team Women's World Cup along with Australia, were not overawed by the occasion as they went on to claim a deserved success thanks to Wilkinson's early second-half goal.
New Zealand had not won any of their 15 previous matches across five previous appearances at the tournament and had set ending that dreadful record as their modest objective this time.
They duly did so against the former World Cup winners, to the delight of a near sell-out crowd of 42,137 fans, a national record for any football match in the country, men's or women's.
Their margin of victory on a cold, wet and windy evening would even have been greater had Ria Percival not missed a late penalty.
Qualifying for the knockout stages from Group A may now be a realistic aim, with Switzerland and minnows the Philippines their other opponents.
Meanwhile Norway, whose squad were woken early by a helicopter and emergency vehicles responding to the shooting just metres away from their hotel, were disappointing.
Wearing all black at the home of the country’s all-conquering rugby union team, New Zealand had been the better side in the first half without creating anything to seriously trouble Norway goalkeeper Aurora Mikalsen.
The breakthrough came three minutes after the restart as Jacqui Hand’s low ball into the box from the right was swept into the net by Wilkinson, the striker based in Australia.
The game opened up as Norway, world champions in 1995, went looking for an equaliser, and Frida Maanum somehow missed the target from a promising position.
Indiah-Paige Riley had a fine effort turned over at the other end, while Norway's former Ballon d'Or-winning forward Ada Hegerberg remained subdued.
Tuva Hansen came closest to equalising with a long-range strike that was tipped onto the bar by New Zealand goalkeeper Victoria Esson.
And it was Hansen’s handball that was then penalised following a VAR check late on, but Percival hit the bar from the resulting 90th-minute penalty.