Park is trying to become the first golfer to win four straight LPGA Tour events since Lorena Ochoa in 2008.
Park was joined by American Irene Cho, Spain's Belen Mozo and South Korea's Hee Young Park and Meena Lee at 65. American Ryann O'Toole and South Koreans Jenny Shin, Amy Yang and Ji Young Oh were three shots off the lead at 66.
Defending champion Brittany Lang opened with a 69.
Stanford closed her late-evening round with three straight birdies to join Matthew atop the leaderboard under mostly sunny skies at Grey Silo Golf Course
''Today I hit it really good,'' Stanford said. ''So it was just one of those days that as a golfer you just love.''
Players took advantage of soft conditions early in the day on the 6,330-yard course. Aggressive approach shots were rewarded before the greens started to dry up in the afternoon.
''We were pretty much able to attack the pins this morning,'' Park said. ''The next three days might be a little bit different if we don't get any more rain, might play a little harder.''
Warm temperatures and sunny skies are in the forecast through the final round of the $1.3 million tournament on Sunday.
The 24-year-old Park oozed confidence as she strolled down the fairways, apparently in complete control of her game on the way to her best first-round score of the season.
''Golf is a sport where you could miss the cut this week and you could win next week,'' Park said. ''There's a lot of imbalance in this game and to keep this kind of level going for four weeks, five weeks, six in a row is a very tough thing to do. We really have to be strong mentally, you have to be physically strong.''
Nancy Lopez holds the tour record with five consecutive victories in 1978, a mark tied by Annika Sorenstam over the 2004-05 seasons. Park, who enters the tournament as the tour leader in seven statistical categories, has already won six times this season.
She's dominating the tour the way players like Sorenstam and Lorena Ochoa did over the last decade.
''At the time when I was watching them, I thought they were so good, that I would never be in that kind of position, never be able to win like four, five tournaments in a row,'' Park said. ''I thought that was toughest thing to do and I'm getting really close to that.
''I'm not as good as them yet, but I'm still learning now and just starting.''