A day after falling five strokes behind with a 74, the 25-year-old Ochoa had eight birdies, an eagle and a bogey before thousands of fans who cheered her every move on the hilly Tres Marias course -- about 175 miles from her native Guadalajara.
The 64 matched the LPGA Tour record on the Jack Nicklaus-designed course where Ochoa won last year. Granada had a 67, and Cavalleri shot a 69.
'I started the day happy and with a lot of will to play and a lot of positive energy. I think that has a lot to do with it,' said Ochoa, who took the top spot in the rankings from the injured Annika Sorenstam on Monday.
'I kicked off well and got a good rhythm going. The big difference is how you start the play. Yesterday, I started with bogeys and missed birdies. Today, I kicked off with birdies.'
Granada, the young Paraguayan who finished second to Ochoa last October at Tres Marias, birdied her final three holes.
'This year is the revenge,' Granada said. 'It's a different situation. I have worked a lot on my play and it's not the first time that I'm playing in Mexico. These are factors that favor me.
'I played well today, finishing with three birdies. I hope that I will continue that streak tomorrow.'
Granada said she wasn't intimidated by Ochoa's vocal fans.
'It doesn't make any difference to me. As a player you don't hear anything,' she said. 'As they say, 'Golf shows that she who plays best wins'.'
Cavalleri, the Italian who started the day tied for first place, had six birdies and two bogeys to stay at the front of the pack.
Pat Hurst (68) and South Korean rookie Na On Min (67) were tied for fourth at 12 under at the course that sits about 6,300 feet above sea level.
Stacy Prammanasudh, the Fields Open winner in Hawaii in February, shot a 70 to join Hye Jung Choi, Kate Golden, Teresa Lu, Sarah Lee, Angela Park and Yu Ping Lin at 9 under.
Ochoa topped the world rankings Monday with 12.84 points, 0.14 points ahead of Sorenstam, sidelined by a ruptured disk in her back. The news sent shock waves south of the border and President Felipe Calderon even made a congratulatory call to Ochoa.
The Mexican star has often struggled in her tournaments in her homeland, but said she's learning to enjoy the attention and pressure.
'You have to be scientific about your mistakes. That way you can work with them and correct them,' she said.
Ochoa said she is planning a more conservative approach Sunday.
'Tomorrow will be a bit different,' she said. 'Basically, it will be a bit more intelligent.'