A three putt bogey at the final hole cost Lincicome the chance of an outright victory and when they returned to the first hole of a playoff Park parred while Lincicome took three to get down from behind the green.
For defending champion Park it was a repeat of last year when she defeated Catriona Matthew at the 3rd extra hole of a playoff.
Park, who won her 6th major championship and 11th LPGA Tour title in the process, will move back to number two in the world behind Stacy Lewis, the New Zealander Lydia Ko now in third position after contending for the title which would have given her the number one mantle.
Ko finished 3rd this week.
Karrie Webb was the leading Australian when she finished 25th.