Mexico outshot the Kiwis 24-7, starting as early as the third minute and including a 14th-minute effort off the bar by Perez. It was frustrated repeatedly by New Zealand keeper Lily Alfed, who denied Samantha Arellano and Taylor Alvarado in the second half.
But Perez tallied the only goal Mexico needed by heading home a corner, one of eight in the match.
Although New Zealand had slightly more possession, Mexico surrendered only one corner and three shots on goal to leave goalkeeper Gabriel Paz will relatively little to do.
The victory was Mexico's second victory at the U-17 Women's World Cup, having lost two of three in their first and only other appearance in 2010.
Mexico next plays Wednesday against Brazil, which reached the quarterfinals in 2010 and won the South American championship in March.