Bowie closed with a 4-under 67, while Park notched a 66 in the final round.
In the playoff, Bowie two-putted for par on the first extra hole, No. 18. Park, meanwhile, ran in a 15-footer to save par and keep the playoff going.
The duo shifted to the par-5 17th at Highland Meadows Golf Club. Bowie pitched her third within one foot of the cup to set up a kick-in birdie. Park on the other hand rolled in a 20-foot birdie putt.
Back to the 18th they went and Park fell apart. Bowie safely found the fairway off the tee before Park's landed in the right rough.
The Korean dumped her second shot into a creek crossing the fairway. Bowie advanced her ball down the fairway safely with her second shot. Park, after taking a drop, lost her fourth shot right off the green.
She took a drop after the ball bounced out of the grandstands and onto a spectator's towel.
Bowie kept her focus while this was happening and dropped her third on the putting surface.
Park pitched her fifth shot over the green. After chipping on, she two-putted for triple-bogey.
Bowie calmly stepped up to her birdie try. She left that putt short, but tapped in for par and her first LPGA Tour title.
Sung Ah Yim fired a 3-under 68 to move into a tie for third at 9-under- par 275. She was joined there by third-round leader Hee-Won Han, who struggled to a 73.
Paula Creamer closed with the round of the day as she shot a 7-under 64 to share fifth place with Jeong Jang at 8-under-par 276. Pat Hurst, Leta Lindley and 2004 champion Meg Mallon were one stroke further back at minus-7.