Pressel, the co-runner-up at this year's U.S. Women's Open, needed 19 holes to beat Mina Harigae in second round play before defeating Jane Rah, 4 and 2, in the third round.
'I could have easily lost this morning,' a relieved Pressel said after beating Rah. 'I missed a few opportunities (today), but made most of the ones I had to.'
Park rolled to a 6-and-5 win over Kimberly Donovan to reach the round of 16, but then fell to medalist In-Kyung Kim in 20 holes later in the day. Kim also beat Park to win this year's U.S. Girls' Junior Amateur.
'She's so solid. She hits every fairway, every green,' Park said of Kim, who birdied the 20th hole for her win in one of three matches that went extra holes in the third round at the Settindown Creek Course of Ansley Golf Club.
Kim advanced to face Angela Park, who was a 3-and-1 winner over Nannette Hill in the third round.
Amanda McCurdy, last year's runner-up, also saw her third round match go extra holes. She was 1-up on Jennie Lee through 17, but found the water to the left of the green on her approach shot at No. 18.
Needing to hole her next shot for a chance to end the match at the 18th, McCurdy landed 10 feet long and Lee putted out for par before winning two holes later. Lee will face Pressel in the quarterfinals.
Alison Whitaker made a miraculous turnaround to put herself in the quarterfinals, winning her last six holes for a 2-and-1 victory over Ryann O'Toole in the third round. Whitaker moved on to face Maria Uribe, who outlasted Ayaka Kaneko 1-up in the third round.
Also advancing was Venezuelan Maru Martinez, who beat Annie Thurman-Young, 4 and 3, in the second round before rolling over Virginia Grimes for a 7-and-6 victory later in the day.
Grimes shot even-par through the first nine holes, but still found herself down by six at the turn.
Martinez will next meet Jenny Suh, who defeated Lorraine Ballerano 1-up in 20 holes in the last match to finish.
With a chance to win in 19 holes, Suh missed right on a very short putt that would have given her the match. But she came back to take the second playoff hole for the win.
Match play continues throughout the weekend and finishes with the 36-hole final on Sunday