Forward Lisa-Marie Utland powered in Norway's second goal of the night in the 34rd minute while an own goal from Falcons defender Onome Ebi in the 37th ensured that the Norwegians went into the break with a 3 - 0 lead.
They face South Korea and hosts France in their remaining group phase matches.
France and Norway have now recorded three points each, while Korea Republic and Nigeria are pointless. Two became three minutes later when the ball was whipped in for Utland, the striker leaning to reach it with her head, Osinachi Ohale's intervention only enough to take it past her own goalkeeper.More news: The next Legend of Zelda is in development
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They are without Ada Hegerberg, the first Women's Ballon d'Or victor, who has refused to play for the national side since 2017 after taking a stand against what she describes as a lack of respect for female players in the country.
The Norway team have won six of the seven opening matches they have played in the FIFA Women's World Cups over the years. Yet still Nigeria pressed and swarmed the home team but, despite a wealth of attacking prowess, couldn't find a way of punishing Norway.
The first penalty came after a handball by South Africa captain Janine van Wyk and the second after follow through tackle by full back Nothando Vilakazi on Garcia which earned Vilakazi a second yellow card and a dismissal.