The extra holes were needed when the pair finished regulation locked in a three-way tie with American Jennifer Song at 15-under 273 after an exciting final round during which nearly a dozen players flirted with the lead.
Park and Lindberg birdied the third extra hole to eliminate Song, who has yet to win on the LPGA Tour.
Former U.S. Amateur champion Song had a golden opportunity to claim a maiden triumph on the second extra hole but her six-foot birdie putt slipped below the cup.
After Song bowed out a hole later with a par, the survivors returned to the 18th one more time and both managed nervy pars in almost total darkness, though floodlights surrounding the green provided some vision.
Looking to win an eighth major of her illustrious career, Park's aggressive long-range birdie putt sped well past the cup but the Korean regrouped and sank a seven-foot par attempt in the gloom to send the tournament to a Monday finish.
"It was really dark on the last playoff hole. Putting in the dark, somehow I was able to make that," Park said.
"I think I was a little nervous because 18 is not my favourite hole. I made some good par saves there to just keep on playing. Finally, we're playing a different hole tomorrow so I'm excited about that."
The playoff will resume on the par-four 10th at 8 a.m. local time (1500 GMT) when the 31-year-old Lindberg will continue her quest for a first major triumph as well as a maiden LPGA Tour victory.
NO NERVES
"I wasn't nervous at all in the playoff," said Lindberg, who carded a closing 71 after starting the day with a three-shot lead.
Park and Song shot matching 67s to join Lindberg one shot ahead of Thai Ariya Jutanugarn (65) and American Jessica Korda (66).
Lindberg, unaccustomed to such lofty heights, surprised many with her poise in the final round of a tournament she has led since Thursday.
"The first few holes I was a little nervous but I settled down and I felt like I was back in business and I kept grinding all day," she said.
"These extra holes, of course I want to be out there beating the girls but it feels like I have nothing to lose. I've been fighting all day. This is just a bonus at the end."
The Swede expects to be equally as calm on Monday.
"(Park) is one of the best female golfers of all time. To have a chance to beat her in a playoff, I think I'm going to sleep great tonight and be ready to go in the morning."
Park added that a good night's rest was key to her chances of emerging with the win.
"I'm just going to have to relax well and go out early in the morning," the 29-year-old said.
(Reporting by Andrew Both in Cary, North Carolina; Editing by John O'Brien)
