The 1995 world champions took the lead when Guro Reiten’s shot deflected off Onome Ebi into the net.
Lisa-Marie Utland fired through the hands of keeper Tochukwu Oluehi to make it 2-0 before an own goal by Osinachi Ohale compounded Nigeria’s misery
Norway are level on points with hosts France, who they face on Wednesday.
Ingrid Hjelmseth, Norway’s 39-year-old goalkeeper, had little to do as Nigeria struggled to carve out chances.
On a bad night for the African champions, defender Faith Michael was carried off on a stretcher after being caught by team-mate Oluehi.