Swaim, playing her final amateur event, broke the tournament record of 137 set in 1999 by Natalie Gulbis, now a rookie on the LPGA Tour. The Sugar Hill, Ga., player holed a 165-yard, 4-iron shot for eagle on the 371-yard 11th hole.
'I was just trying to make it to match play,' said Swaim, a member of the United States' winning Curtis Cup team two weeks ago in Pittsburgh. 'Since this is my last amateur event, I wanted to enjoy myself ... and I did.'
She credited local caddie Terry Cook for her eagle.
'I wanted to hit a 5-iron, and he called me off it and said to go with a 4,' Swaim said. 'I did and it went into the hole. Without him, my scores wouldn't be that good.'
Meredith Duncan, the defending champion who also will turn pro after the tournament, had an asthma attack on the seventh hole as the temperature soared into the high 90s.
The former LSU star shot a 79 for a 147 total, four strokes better than the cut of 151 as 64 players advanced to match play on the Sleepy Hollow Country Club course.
'I'm all right now,' said Duncan, of Shreveport, La., 'I panicked and that made it worse. I felt as if I couldn't breathe. ... I'll be fine for match play.'
Danielle Downey of Spencerport, N.Y., Swaim's former Auburn teammate, shot her second straight 69 to qualify second at 138. She holed a 7-wood shot for a double eagle on the 453-yard, par-5 eighth hole.
'The hole was in the shade so I didn't see it go in, but my two sisters [Erica and Melissa] did and they went nuts,' Downey said. 'Playing this well got me a good seed. The better the seed, the easier it is to advance.'
Carol Semple Thompson, the 53-year-old player seeking her seventh U.S. Golf Association title, shot a 67 -- the best round of the day -- to match South Korea's Aree Wongluekiet and Canada's Alena Sharp at 139.
'My experience matters a great deal,' said Thompson, the Sewickley, Pa., player who won the 1973 tournament for her first USGA title. 'I know I'm never out of a round. Anything can happen the last four or five holes.'
Wongluekiet and Sharp both shot 69s. Wongluekiet's twin sister, Naree, also advanced, shooting a 70 for a 144 total.
U.S. Girls' Junior champion In-Bee Park and NCAA winner Virada Nirapathpongporn qualified for match play.
The 14-year-old Park, from Eustis, Fla., shot a 70 for a 143 total. Nirapathpongporn, the Thai player coming off her sophomore season at Duke, had a 68 for a 145 total.
Comedian Bill Murray, a Sleepy Hollow member, caddied for Kailin Downs after her assigned caddie failed to show up. Downs, from Bend, Ore., shot a 73 for a 151 total, then lost in a 15-player playoff for the final two spots.
'I was enormous. She couldn't have done it without me,' Murray said. Paula Creamer of Pleasanton, Calif., and Elizabeth Janangelo of West Hartford, Conn., birdied the playoff hole to advance to match play.