Referee Bakary Gassama consulted the video assistant referee before issuing three yellow cards to Reyes, Herrera and Boxall.
The Mexicans, who saw Ryan Thomas denied an 85th-minute equaliser by the woodwork, survived a major scare after Chris Wood had fired the Kiwis into a half-time lead and then squandered a series of further chances before Raul Jimenez and Peralta spared their blushes.
Mexico head coach Juan Carlos Osorio apologised for losing his temper during the match.
The 56-year-old had a heated argument with one of New Zealand’s assistant coaches after Mexico’s Carlos Salcedo went down with a shoulder injury in the first half.
And the Colombian coach later had to be restrained by his own bench during the brawl in injury time.
“I would like to apologise to our fans, the way I spoke to one of their assistant coaches was not OK,” he said.
“There is no place for disrespect in football and I am sorry. The game was rough, almost violent on occasion, so I lost my temper.”
New Zealand’s head coach Anthony Hudson played down the incident.
“I thought it was bizarre really, it was like we had elbowed the player the way it was going on,” he said.
Mexico, who left striker Javier Hernandez on the bench, top the group ahead of Portugal on goals scored.
Mexico now only need a draw against Russia in Kazan on Saturday to be sure of reaching the semi-finals.
Hosts Russia are third in the group while New Zealand remain bottom and are out of the tournament.