Stanford finally blinked on the deciding playoff hole and Park kept her birdie streak alive for the victory at the Manulife Financial LPGA Classic.
Both players tied the LPGA Tour record for lowest total score at 26-under 258. It would take three playoff holes – all on the 471-yard, par-5 finishing hole – before Park ended the drama by hitting a short putt for her second career LPGA victory.
''When we started (the) final round, I just kept reminding (myself) this is just another round,'' Park said. ''It doesn't matter (if it's the) final round or a first round, keep it simple and just think about always (hitting) my target.''
She hit the target when it counted, reaching the green in two on the deciding hole. Stanford, meanwhile, needed three shots to get on the back fringe and her long birdie putt ended up a few feet short.
Park hit her 45-foot eagle putt to within a few feet of the cup. She made the birdie, raised her fist in the air and later threw the ball into the grandstand surrounding the green.
The effort capped a remarkable week for the 26-year-old South Korean, who recorded a career-best 61 on the par-71 course a day earlier. Stanford closed with a 64, while Park, who had a one-shot lead on the American after three rounds, had a 65.
''If somebody would have told me you're going to shoot 64 today and not win, I would have thought they were crazy,'' Stanford said. ''So for me to shoot 64-64 on the weekend, you know, it's good for me but it's not a 'W,' so you play to win.''
Matthew made a move early in the round. She picked up her third straight birdie on No. 7 to move into first place, leaving Stanford and Park a shot behind.
The trio quickly moved ahead of the pack as they approached the turn.
Matthew birdied Nos. 11 and 12 but a bogey on the 15th hole snuffed her momentum. Stanford had seven birdies over a bogey-free round, while Park went on a tear with three birdies over her last four holes heading into No. 18.
That set the stage for a showdown that would last about an hour.
Sitting tied at 25 under after 71 holes, Stanford reached the green in two and two-putted for birdie. Park pushed her approach shot wide and hit a nice chip from beside the grandstand to within 4 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 8 feet from the cup. She pushed her eagle putt wide and settled for birdie.
Stanford chipped on from beside the fringe and made 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 3 feet and Park did the same before both players made 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 4-wood to get out but didn't hit it cleanly, with the ball landing in a fairway bunker. Stanford did well to get it to the back fringe but with Park already lying 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 get 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.''