Kim and Chia each carded two-under-par 34s, but Kim won the card-off. Kim birdied the ninth hole and Chia, the reigning All-Area Girls' Golfer of the Year, recorded a par on the par-four final hole.
"Playing against the other players in our league motivates me to do better," Kim said. "It's the second time that I've played this course and you have to pay more attention to your short game.
"I felt like my short game was real good. I went our there and tried to enjoy every shot and not put too much pressure on myself."
Chia, who helped the Falcons place third with a team score of 163, said her short game helped her turn in a low score.
"I went out there and played everything safe," Chia said. "I had a good short game that helped me out a lot.
"A round like this gives me even more confidence because I know that I can shoot better."
Palos Verdes won the event with a 152, followed by Sherman Oaks Notre Dame (153). Burroughs took fourth with a 167 and Thousand Oaks Redondo Beach was fifth (169). San Marino tied with Torrance for 10th at 176, Burbank was 12th (179), La Cañada placed 13th (183) and Westridge finished 18th (204).
Megan Cormier of Redondo Beach shot a two-over-par 39 to win the B Flight competition. Cormier edged Arcadia's Adrienne Lao in a card off.
Irene Maemura finished with a 37 in the A Flight to lead Burbank.
"She's just a freshman, but Irene can go far," said Burbank Coach Branco Sevak, who received a 40 from Tess Apinchapong. "I'm pleased with the way we have been playing.
"The Pacific League coaches were joking around before that we should have made this a league match."
San Marino got a 36 from Tiffany Gu and a 42 from Camille Wang.
Joany Gao had a 36 for Burroughs, which got a 38 from Ravipa Losakul.
"You always want a good showing," Burroughs Coach Greg Everhart said. "There are some real solid golfers in the tournament.
"I was impressed with the way Joany played in shooting even par and I think having all of the Pacific League teams here shows the strength of our league. You had the top-two finishes in the A Flight from the Pacific League."
Crescenta Valley received a 41 from Audrey Chung, a 42 from Deborah Chin and a 46 from Amy Park. May Lo carded a 42 for La Cañada.
Westridge's best scorer was Jackie Pai, who finished with a 46.