Park, a 15-year-old from Eustis, and Lincicome, 18 from Seminole, shared medal honors at The Country Club at Heathrow, finishing 36 holes at 1-over 145.
Estill made a 9-foot birdie putt on the second playoff hole to beat Maru Martinez and claim the fifth and final qualifying spot for the Open on July 1-4 at The Orchards Golf Club in South Hadley, Mass.
'I'm real excited,' said the 41-year-old Estill, who will be playing in her eighth Open. 'Thirty-six holes, even when you've been on tour for 13 years, is a lot of golf.'
Estill and Martinez tied at 4-over 148.
Brittany Luse, of Orlando, was third at 146, Kristin Tamulis, of Naples, Fla., was fourth, one stroke back.
The qualifier was completed Tuesday after rain and lightning stopped play on Monday.
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