Despite being outshot 33-17 for the 120 minutes, Mexico had chances to win the match, putting a corner kick off the crossbar in the first minute of second-half injury time and Yamile Franco hitting the frame with a free kick in the 99th.
Nigeria finally scored the go-ahead goal with Oparanozie arcing a header from Ugo Njoku's cross over Mexican goalkeeper Cecilia Santiago.
This was the second consecutive time Mexico has been eliminated in the quarterfinals, having been beaten by South Korea 3-1 two years ago. It also was the second straight time Nigeria has eliminated a CONCACAF opponent in the first knockout round. It needed penalties to subdue the United States in 2010.
The result leaves only one CONCACAF team remaining in the U-20 Women's World Cup. The United States will face North Korea on Friday, with the winner to face Nigeria.