Sitting tied at 25 under after 71 holes, Stanford reached the green in two and hit a two-putt for birdie. Park pushed her approach shot wide and hit a nice chip from beside the grandstand to within four feet before draining the birdie putt to force a playoff.
The players hopped into golf carts and returned to the tee to keep playing the hole until there was a winner.
Park had a chance for eagle on the first extra hole, hitting a beautiful approach that bounced once before settling eight feet from the cup. She pushed her eagle putt wide and settled for birdie.
Stanford chipped on from beside the fringe and hit a short putt for a birdie of her own.
On the second playoff hole, both players landed in the first cut beside the green. Stanford went first and chipped it within three feet and Park did the same before both players hit their putts.
Stanford was unlucky on the third playoff hole as her tee shot found the rough and settled into a depression.
"By far the worst lie I had all week," she said.
She used a four-wood to get out but didn't hit it clean, with the ball landing in a fairway bunker. Stanford did well to get it to the back fringe but with Park already laying two, Stanford needed to chip in to force play to continue.
When her ball settled a few feet from the hole, Park had the opportunity to go up and down for the victory and she took advantage.
"I did everything I could, it just wasn't enough," Stanford said.
Park earned $195,000 for the win. Stanford picked up $120,353 of the $1.3-million tournament purse with the runner-up finish.
Scores were low for all four rounds as players took advantage of wide fairways and greens that remained moist after heavy rain earlier in the week.
South Korea's Meena Lee (66) was fourth at 20 under and Karine Icher of France (63) was another shot back in fifth place. American Michelle Wie closed with a 66 to finish tied for 16th place but was still 11 strokes off the pace.
"It's pretty crazy that you shoot 15 under and you're not in the top 10, you know," Wie said. "It's a birdie-fest out there."