Davies, who earlier this year won the inaugural U.S. Senior Women's Open, had a lost ball on the par-5 18th hole on The Pete Dye Course at French Lick Resort. She still salvaged a bogey in chilly, windy weather that had the 55-year-old from England bundled up in a blanket between shots.
Inkster, runner-up to Davies at the Senior Women's Open, made eagle on the closing hole for a 69.
Jane Crafter was at 70. Defending champion Trish Johnson opened with a 73.
Temperatures were in the high 40s, but the damp air and wind made it feel even colder.
Inkster made a bogey on the 17th hole by missing the green with a 9-iron.
"As old as I am, I still get made and I crushed that drive on 18," said Inkster, who followed with a 3-wood to 15 feet to set up her eagle.
The 54-hole event concludes Wednesday.
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