Six minutes later, Osinachi Ohale poked the ball into her own net from a cross.
Nigeria was hurt when defender Faith Michael was stretchered off after a collision with her goalkeeper early in the second half.
In 105 games with her French professional team, Hegerberg has been electric as she has scored 130 goals since 2014 and became the first women's player to win the Ballon d'Or Feminin (the best women's football player of the year award by French Football) in 2018. 19-year-old Giulia Gwinn was the scorer of the winning goal in the 66th minute after the Chinese had wasted a couple of gilt-edged chances in the first half.
They face South Korea and hosts France in their remaining group phase matches.
The goals were scored in the first half to condemn the nine-time African champions to their 17th defeat in World Cup finals.
"We're going to enjoy this victory a little bit and then we're going to travel to Nice to meet another world-class team [France]". We will try to make counter-attacks against France.
"When it comes to sport, never ever give up. I go out there and play football, help the team, help my team-mates, get some goals if possible". We have to fight for 180 minutes more, plus added time. "You must give it your best", the coach told the players after their last training session at the Stade Jean Bouchon in Reims ahead of the tie against Norway.
Nigeria are the only African side to have appeared in every Women's World Cup, and Norway have also featured in every tournament.
The 2019 FIFA Women's World Cup will run from June 7 to July 7.
Nigeria impressed but were unable to progress to the knockout stages at the 2015 World Cup after a tough draw that grouped them with eventual champions USA, Australia and Sweden.
The game petered out late on, with Norway only having one shot on target in the second half.