The South Korean approached the final two holes trailing Brittany Lincicome by two shots, but a birdie on 17 and a vital 15-foot par putt at the last gave her a two-under 70 and meant she caught her rival at 11-under 276 after the American bogeyed 18 to complete a 71.
It left the pair to replay the 18th, the toughest hole of the course at Monroe Golf Club. Lincicome chipped six feet past the hole after knocking her approach to the left, and then failed with the putt, while Park, after finding the rough behind the hole with her second shot, chipped to three feet and coolly sank the putt.
Park's second play-off win in the championship halted a run of three straight major wins for players from the United States this year. The 26-year-old admitted her 2013 experience - she took three extra holes to beat Matthew - had come in handy when it mattered most.
"I didn't feel that nervous at all when I was just playing the final round," she said, "but once I got to the tee on the play-off hole, I just felt the nerves right away, and it was like a replay of last year. Experience helped me out, and I was able to stay calm."
Lincicome, on the other hand, was inconsolable after missing out, but hoped to get back on track next week at the Canadian Pacific Women's Open in Ontario. "Lots of tears," she said when asked about her emotions. "It was so close, and [I'm just] another step behind. Maybe next week in Canada is my week."