Korda, a Bradenton native, nabbed her ninth career LPGA victory despite squandering a four-shot lead to start the Sunday.
After Korda and Ko returned to the par-4 18th hole for the playoff, and made par the first time through, Korda's approach shot on the second go-round at the hole rolled off the back of the green toward the hospitality tent.
Ko landed her shot on the green, but after Korda chipped on, Ko's long birdie putt stopped several feet short.
The New Zealander then watched her uphill par putt lip out. Korda calmly delivered her six-footer to the centre of the hole before celebrating with the home crowd.
"Even when I was down, they were so, so positive and keeping me in it," Korda said on the Golf Channel broadcast.
"It was just such a grind out there, so back and forth. I can't even believe it right now."
Ko and Korda took much different paths to finish 72 holes in 11-under 273. Ko posted a two-under 69 on Sunday and Korda signed for a two-over 73.
Korda went one-over on the front nine, and her hopes took a blow with a bogey-double bogey-bogey stretch from 14 to 16.
Ko then made a remarkable eagle at the par-5 17th hole to take the lead. Her second shot narrowly avoided water, bounced up onto the green and rolled to inside a foot of the hole.
Soon after Ko's tap-in eagle, Korda made her own eagle putt at 17 from nearly off the green.
Ko parred 18, meaning Korda needed birdie to tie. She dialled up an approach shot that nestled within inches of the pin, necessitating the playoff.
"I honestly thought that the tournament was over going into 17," said Korda, 25.
"I just kinda gave myself a chance. I knew that if I got that eagle in, I'd have to birdie the last hole. I always seem to make it very dramatic and interesting. There's no better feeling to do it in front of a home crowd."
Australia's Robyn Choi began the day five shots off the pace but faltered with a six-over 77 to tie for 16th at two-under.
Megan Khang took a one-over 72 to finish third at eight-under.
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