As the mercury tipped 100 degrees at Pumpkin Ridge Golf Club the pair shot 7-under 65s to top the leaderboard by a stroke.
Sitting behind them were Cristie Kerr, Inbee Park and Pornanong Phatlum after the opening day of action in North Plains.
Last week's Toledo Classic winner Yeon Ryu was a further shot back along with Brittany Lincicome, Alison Walshe and Jee Young Lee.
World number one Yani Tseng had a 70 while defending champion Suzann Pettersen shot a 71.
Michaels made birdies on the opening four holes when temperatures were slightly cooler, although she still managed two more birdies on the final three holes.
Japanese player Miyazato said: "My golf game is very confident right now.
"To begin the season, I was not so very good with my golf game. I start to shoot right in the last couple four, five events. I'm gaining more confidence."
Mariajo Uribe delighted spectators with a hole-in-one on the 169-yard third hole on her way to finishing with 71.