Smith carded a second straight five-under 67 to move into 10 under at the Shoal Creek Golf and Country Club in Alabama.
Featuring the USGA's new two-hole playoff, Kim holed a lengthy putt on the first additional hole (the 14th) to stun Jutanugarn, but a dropped shot on the 18th paved the way for even more golf, with the former Women's British Open champion recording a pair of sturdy pars.
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.
American Danielle Kang (69) was four shots back of Ciganda in solo fourth. She made six birdies and just one bogey, rarely encountering serious trouble.
Tiger Woods hit the ball well enough to be up there with them at Muirfield Village, except for missing five putts inside 7 feet.
"Well, I haven't been in the position before, I but I hope to show up like it's another day", said Smith.
Of the other two overnight leaders, Lee Jeong-eun backtracked with a 75 to fall eight strokes back, while Jutanugarn, who had a late tee time, will have to complete her second round early on Saturday morning.
With a 10-under 134 halfway total, Smith enjoyed a nice buffer over compatriot Su Oh, who eagled the par-four 15th en route to a 68 for six-under 138.
"I think I'm going to sleep well tonight", Ariya said. While there have been glimpses of strong play this season, like a 67 in the third round of last week's LPGA Volvik Championship and a 67 in the final round of the HSBC Women's World Championship, her best finish is a T26 at the Kia Classic. He missed the green from the fairway on the 18th on the first extra hole and had to scramble for par.
Anyone who watched surely enjoyed the affair, and they may also have been clued into a specific visual: Jutanugarn applauding successful shots made by Kim during their one-on-one playoff.
"I never had that final putt to win".
After sharing the overnight lead, Smith quickly took advantage of benign early conditions to pick up five birdies on her outward half at Shoal Creek.
"Honestly I tried to smile", she said. "I didn't sleep much last night and I'm really exhausted".
Joaquin Niemann, the 19-year-old from Chile, birdied the 18th hole to tie for sixth. "He's like, 'Come on, do you want to win?' I'm like, 'Yes.' He said, 'Okay".