The leading pair shot eight-under 63s to top the leaderboard, two strokes ahead of world number one Inbee Park, who is attempting to become the first player to win four straight LPGA events since Lorena Ochoa in 2008.
Irene Cho, Belen Mozo, Hee Young Park and Meena Lee all joined Park on 65.
Stanford finished her opening round strongly with three birdies at the end of a sunny day 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."
Park said: "We were pretty much able to attack the pins this morning. The next three days might be a little bit different if we don't get any more rain, might play a little harder."
"Golf is a sport where you could miss the cut this week and you could win next week," she added. "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."