The regulation time and extra time ended 0-0 as both teams failed to find any breakthrough.
Desire Oparanozie and Michelle Alozie missed from the spot for the Super Falcons.
Rasheedat Ajibade and Christy Ucheibe converted for Randy Waldrum’s men.
Beth England, Rachel Daly and Alex Greenwood converted for the European champions, who had a player sent off in regulation time.
England played with 10 women through extra time after forward Lauren James, their top scorer with three goals in the group stage, was sent off in the 87th minute for an ill-tempered stamp on the back of Michelle Alonzi after the two went down in a tangled heap.
Fourth-ranked England face either Jamaica or Colombia in the quarter-finals in Sydney on Saturday.
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