Jutanugarn fired a one-over 73 at the Shoal Creek Golf and Country Club in Alabama to finish at 11 under, with Kim (67) joining her.
This is the first time the USGA has gone to a two-hole aggregate playoff, and Kim quickly took command by rolling in a long birdie putt on the 14th hole.
On the fourth and final playoff hole, both players had bunker shots with Kim leaving hers 15 feet from the hole while Jutanugarn produced a moment of brilliance as she hit hers to 18 inches. Jutanugarn, already a nine-time victor on the LPGA Tour and the 2016 British Open champion, appeared under no pressure whatsoever when beginning her final nine holes.
But by the time thunderstorms and bad light forced an early halt to the day's play, with nearly half the field still on course at Shoal Creek, the cut line had dropped to four-over.
But her lead dwindled to just one as she headed to the final hole of regulation, where her long putt to win failed to drop.
Kim would have completed the largest final round comeback in the 72-year history of the US Women's Open. "I'm pretty sure tomorrow is going to be a pretty good day". I think I rushed putting them in.
"I have to give myself more opportunities at birdie because I feel quite good about the putter", Park said. Jutanugarn had her lone birdie of the back nine at No. 16, but bogeys at Nos.
Argentina friendly called off after Palestinian 'threats, provocations'
The two-times World Cup winners face Iceland, Nigeria and Croatia in what is considered to be one of the hardest groups in the tournament.
At the par-5 11th, Ariya took dead aim at the hole from 200 yards with her second shot and crushed a four-iron that nestled up to within 12 feet of the hole, and while she missed the eagle putt, the birdie built further momentum. So it's nice to be able to feel like I'm seeing the greens really well and seeing some putts go in. "I didn't sleep much last night and I'm really exhausted".
She opened the day in a three-way tie atop the leaderboard with Jutanugarn and Korean Jeongeun Lee.
Having been way ahead following an imperious display, a treble-bogey seven on the 10th dramatically shifted the dynamic of the occasion, before bogeys on the two closing holes saw the 22-year-old Thai golfer slip into extra holes with Kim of South Korea, who herself had shot a metronomic 67 on Sunday.
She carried the meltdown through with back-to-back bogeys on 17 and 18.
Second-placed Ariya said she was paying little attention to her position, instead just focusing on her own form.
Defending champion Park Sung-hyun missed the halfway cut with rounds of 76-77, and world number two Feng Shanshan of China also exited early after rounds of 78-74. In his day, he said, when players competed for major championships, you would not have seen them applauding a good shot from a competitor.