South Korea's Ko, who was tied eighth before the third round, got off to a strong start as she birdied four of her first five holes.
She managed another four against a lone bogey and moved to a 14-under par total of 202 after another weather-delayed day in Singapore.
American Korda's consistency continued as she carded a third straight four-under 68 to remain in contention after finishing one shot ahead of compatriots Allisen Corpuz and Elizabeth Szokol, who were tied for third place with a two-under 70.
Szokol, the leader after Thursday's first round, had another inconsistent day after mixing five birdies with three bogeys, while Corpuz drained six birdies but suffered a setback on the fifth with a double-bogey.
Overnight leader Danielle Kang slipped to fifth with a 72 while top-ranked Lydia Ko (70) of New Zealand was tied for 13th with Japan's Yuka Saso (72) after a round of two-under 70 to be seven-under for the tournament.