"It was the match of my life," the 28-year-old Ochoa said. "To do it in a World Cup, in front of all the fans, it's incredible."
However, Ochoa wasn't the only goalkeeper in form at Fortaleza. Just as the World Cup hosts were successfully stifled, Julio Cesar of Brazil kept his clean sheet with some impressive saves.
Ochoa twice denied Neymar, diving at full stretch to turn the Brazil striker's header round the post in the 26th minute and then blocking his shot in the 69th.
"The (Neymar) header was the most complicated. It was a hard header and close to the post ? that was my favorite save," Ochoa said.
Four minutes before the end, Ochoa pulled off another superb save to block a header from Brazil captain Thiago Silva after he met a free kick from Neymar.
After referee Cuneyt Cakir blew the final while, Mexico players lined up to hug Ochoa, who plays at French club Ajaccio.
"I can't remember another Mexican goalkeeper doing such a great job in the World Cup," coach Miguel Herrera said. "I'm happy for any player to have that role, but tonight, Memo was the hero."
With Mexico on four points from two games, the same as Group A leader Brazil, Ochoa's saves have kept his team on course for the second round.
"Things went our way and now we've got to keep going," he said.
Mexico relied largely on counterattacks and shots from distance to fend off Brazil, for whom Julio Cesar was also decisive.
The 34-year-old keeper, who played most of his professional career at Inter Milan, is currently with Toronto FC. But the Brazilian showed no sign of losing his sharpness.
Hector Herrera aimed the ball under the Brazil crossbar in the 24th minute, but Julio Cesar tipped it over with an athletic save before later stopping a low shot by substitute striker Raul Jimenez in injury time.
Brazil coach Luiz Felipe Scolari said he was pleased with his team's performance, but had no doubts about the reason for its failure to win.
"I didn't like their goalkeeper because he was spectacular," he said. "He was calm and confident, and for me he was the man of the match."