The four-day biennial event, which is being held at the Jack Nicklaus Golf Club Korea in Incheon, west of Seoul, pits four players from eight countries against each other in four-ball and singles formats.
South Korea lead Pool A on four points, one ahead of England after their quartet of Charley Hull, Georgia Hall, Bronte Law and Jodi Ewart Shadoff won one match and halved the other against Australia.
Cristie Kerr and Lexi Thompson got the U.S. on the board in Pool B with a 2-up win over Pernilla Lindberg and Madelene Sagstrom but Sweden hit back through Anna Nordqvist and Caroline Hedwall, who beat Michelle Wie and Jessica Korda by the same score.
Kerr, who has played in the two previous editions of the Crown, thanked her partner for carrying the partnership as she struggled with her swing.
"It wasn't pretty today, I didn't contribute that much," she told reporters. "When I was out of it, which was probably three quarters of the day today, Lexi was in there."
Thailand, who chose to split up sisters Moriya and Ariya Jutanugarn, top Pool B after beating Japan in one match and halving the other.
U.S. Women's Open champion Ariya, the younger Jutanugarn, said she tried to make partner Sherman Santiwiwatthanaphong loosen up a bit after their first tee shots.
"I'm like, our goal is we're not going to be scared. We're just going to hit, because I trust you," she said. "You have to trust me. Like, don't be scared."
World number one Park Sung-hyun partnered fellow major winner Kim In-kyung to a 1-up win for the top-ranked Koreans before Chun In-gee and Ryu So-yeon won their match 2-up.
Big-hitting Park drove the green at the par-four 14th, which measured 263 yards on Thursday, then holed her putt for eagle to set Korea on their path towards victory.
Organisers, concerned about the impact of approaching Typhoon Kong-rey, said on Thursday that the third round of matches would begin as soon as the second slate of ties had been completed on Friday.
(Reporting by Peter Rutherford; Editing by John O'Brien)
