Kim, the overnight leader, looked to have blown her chance of victory after finding water with her tee shot at the 18th, with her South Korean compatriot Park setting up a birdie putt to claim the $270 000 winners purse.
But Park missed and Kim confidently took out the flag and chipped in from the side of the green to force extra holes after the duo were locked at 11-under-par 277.
They then replayed the 18th with Kim this time finding the fairway before firing a short iron straight at the flag, just clearing the water hazard, bouncing twice and then nestling at the bottom of the cup for an eagle two.
Looking into the setting sun on Oahu, Kim and Park seemed unaware of the outcome at first before the 22-year-old broke out in laughter as she high-fived her caddie in celebration.
It was the 22-year-old's second LPGA Tour win of the year following victory in Bahamas in February.
Kim's win, following her final round one-over 73, was the sixth by a South Korean in nine events on Tour this year.
Park, winner in Singapore in March, shot a final round 71 as gusty winds again made scoring tough.
Kim In-kyung (74) was third on nine-under, with Choi Chella (72) and Kim Hyo-joo (69) fourth on 281.
German Sandra Gal was the top non South-Korean finisher after shooting a final round 69 to finish sixth on six-under.
Original source: Kim wins LOTTE Championship