Jutanugarn was cruising to a comfortable victory after an outward 32 gave her a seven-shot advantage, but she frittered away that lead with a series of mistakes after the turn, beginning with a triple-bogey seven at the 10th.
South Korean-born Su-Hyun Oh, who moved to Australia at the age of eight, shot a 68 and is third.
"I felt really good and kept my nerves under control, but I think the nerves showed up in my putting", she said. "I don't know why".
"She rolls the ball beautifully".
New Zealander Lydia Ko struggled to a round of 77 and is now on the cut-line. "After she become world No1 last time she struggled", explained the Jutanugarn Snr.
"I know everything's going to be the same and they're going to love me the same, " Jutanugarn said. Lee fell back to 2 under with a second-day 75. Her first Major win was the British Open in 2016.
Smith has played 5-under on the back nine holes each of the first two days and settled for par on the front.
The format for the playoff was a two-hole aggregate on 14 and 18, but the players were still tied after the two holes.
Jutanugarn then flew the green with her approach to 18 while Kim's came up short and found the front-left bunker, from where she was unable to get her escape close to the hole and two-putted for bogey while her Thai opponent played a delightful pitch and converted from four feet to force sudden death.
The players went back to the 14th, which they both parred. Kim's shot out of the bunker was decent, but Jutanugarn's was phenomenal, rolling right next to cup and setting up an easy par putt.More news: Sara Gilbert Sad For People Who Lost Jobs Due To ‘Roseanne’ Cancellation
Jutanugarn was far from flawless but kept her card clean by saving par at the picturesque par-three fifth by sinking a six-foot putt.
Duane was speaking after his 33-year-old wife carded a second straight 67 to leave the field in her dust in the second round at Shoal Creek.
"After you have a seven-shot lead and end up that you have to go to play-off, you have no expectations", the champion admitted.
But things were about to get rough in a hurry. The third round begins with groups of three, starting on the first and tenth tees.
She was at 12-under 204 for the tournament.
While Jutanugarn was fading, the 22-year-old Kim was rolling. She missed several good chances to pick up shots, which appeared to take the wind from her sails, before surrendering the lead with consecutive bogeys at the eighth and ninth holes. Like everyone else, she was shocked she was still in contention.
"I hit a couple squirrelly shots (late in the round), but made some nice up-and-downs. I'm pretty sure tomorrow is going to be a pretty good day".
Smith started the tournament with back-to-back 67s, but shot a 74 in the third round and didn't make a birdie to fall into second place.