Stanford birdied 10 holes, shot a 62 and set an 18-hole record for the Superstition Mountain course. It was her lowest score on the tour by two shots.
"I guess that's what they call the zone. I found it today," said Stanford, whose only win came five years ago. "It was one of those days that you can't even get in your own way."
Stanford, who lost to Hilary Lunke in a playoff at the 2002 U.S. Women's Open, was out in front of world No. 1 Lorena Ochoa.
Ochoa's 65 put her in position to win this tournament for a second straight year.
Stanford shot a 6-under 30 on the front nine.
"I looked up and it said six (under) and I thought, 'I've only played nine holes.' That was the first time that it hit me," she said.