Without Ballon d'Or winner Hegerberg, who quit international football in 2017 due to a dispute with her home federation, the 1995 champions relied on goals by Guro Reiten, Lisa-Marie Karlseng Utland and an own goal by Osinachi Phale to prevail.
The result put Norway in second place in Group A behind hosts France, who thrashed South Korea 4-0 on Friday in the opening game of the month-long tournament in Paris.
Reiten put Norway in front after 17 minutes when she volleyed home from a corner.
Utland doubled the tally with a powerful shot from close range after being set up by Reiten in the 34th.
Three minutes later, three-times African champions Nigeria were completely overwhelmed as Ohale deflected Isabell Herlovsen's cross into her own goal.
Norway next face France in Nice on Wednesday while Nigeria take on South Korea in Grenoble the same day.
(Reporting by Julien Pretot; Editing by Ed Osmond)
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