World number one Park won on the third hole of the playoff at Locust Hill Country Club outside Rochester, New York, with a birdie on the par-four 18th hole after both parred the first two sudden-death holes.
The two golfers, who tied at five-under-par 283 after regulation, played 39 holes in a marathon finishing day at the weather-delayed championship, getting in the entire third and fourth rounds on Sunday and then the three-hole playoff.
In contrast to the final round, in which Matthew played impeccably with four birdies in a bogey-free tour of the tree-lined course for a 68 and Park struggled finding the fairways for a 75, the Korean had the steadier hand in the playoff.
Park, who missed eight fairways in the final round and struggled out of the deep rough, regained her swing on the tee and split the fairway on the decisive playoff hole, while Matthew landed in the rough behind a large tree right of the fairway.
After the Korean put her approach safely on the green, the 43-year-old Scot punched out through the fairway and into rough short of the green. Her next shot also failed to reach the putting surface and then she chipped up weakly below the hole.
Park then rolled in her birdie putt for her third major triumph and second of the year following her victory in the Kraft Nabisco.
"It was one of the toughest days out there," Park, 24, said in a television interview on the green after her winning putt.
"I actually thought I was very lucky to get into the playoff," added the Korean, who had led by three shots before bogeys on three of the last five holes of regulation.
"I just hit it everywhere, I wasn't hitting fairways. I finally did hit three fairways in the playoffs, which helped me a lot.
"It was a tough day out there. I'm so tired."
Tied for third place on four-under-par 284 were American Morgan Pressel (75) and Norway's Suzann Pettersen, who fired a seven-under 65 in the final round, the best score of the tournament.
(Reporting by Larry Fine in New York; Editing by Gene Cherry)