Guro Reiten opened the scoring with a deflected shot in the 16th minute before Lisa-Marie Utland doubled their lead just after the half-hour mark with just her fifth touch of the game.
Norway had their third goal in the 36th minute thanks to an own goal by Osinachi Ohale when she poked the ball into her own net after a cross from the right.
Faith Michael's faint touch was enough to put the ball out of Utland's reach before the Nigeria defender collided with her goalkeeper and was taken from the pitch on a stretcher.
Nigeria goalkeeper Tochukwu Oluehi spilled the ball late in the game and it trickled out for a corner, but the African side defused the threat.
Nigeria continued to push forwards in the six minutes of stoppage time in a bid to score a morale-boosting goal, but they came away empty-handed.
Also on Saturday, Germany beat China 1-0, while Spain ran out 3-1 winners against South Africa.
Germany coach Martina Voss-Tecklenburg praised the performance of her young players after they began their Women's World Cup campaign with a narrow victory.
Teenager Giulia Gwinn scored the only goal of the game in the 66th minute but the Germans rode their luck with Yang Li hitting the post shortly before the half-time break.
Voss-Tecklenburg said: "The young players who fought through this match now have the experience and know what it is like to play a World Cup match.
"We have realised that a World Cup match is different to the training sessions. Some things happened that were not great, but we are in this World Cup and we want to go as far as we can."
Saturday June 8
Group B: Germany 1-0 China
Group B: Spain 3-1 South Africa
Group A: Norway 3-0 Nigeria
Sunday June 9
Group C: Australia vs Italy (1200, Valenciennes) - BBC red button/website
Group C: Brazil vs Jamaica (1430, Grenoble) - BBC red button/website
Group D: England vs Scotland (1700, Nice) - BBC One