The 31-year-old tournament, one of the more popular stops on the women's golf circuit, has become a victim of the recession. Tournament officials announced last month the event would not be held after this year.
Corning Inc., manufacturer of glass and ceramic products, is the longest continual sponsor of an LPGA Tour event.
Park and Icher both shot an 8-under 64 on a perfect day for golf at the Corning Country Club.
Sarah Lee, Minea Blomqvist, Soo-Yun Kang, Hee-Won Han and Sandra Gal were all at 65. a large group at 66 included Paula Creamer and Morgan Pressel.
"If you're not motivated to win this week, then I don't know what gets you motivated out there," said Creamer, who tied for second place in 2007. "They've been doing this for 31 years. It's amazing."
Michelle Wie, in her first year as a tour member, has not missed a cut in her first six appearances this season. She was in danger of doing so this week, however, after shooting a first-round 73 that left her tied for 103rd place.
Swim Week Miami Beach 2014 [PHOTOS]