Korda had seven birdies at Liberty National in Jersey City, New Jersey, for a 54-hole total of 13-under 203.
Green, meanwhile, had nine birdies in a nine-under-par 63 that put her alone in second on 11-under 205.
Korda is aiming to get back in the winner's circle after seeing her record-equalling streak of five victories in five LPGA starts to end at last week's Founders Cup.
She started day three off the lead and methodically made her way up the leaderboard, notching birdies at the second, fourth and seventh holes.
Coming in she birdied the 10th, 13th, 15th and 16th to power into the lead, maintaining her rhythm despite changing conditions.
"First nine the wind was down, it was sunny, it was warm," she said. "By the time we got near to the water on the back nine the wind started picking up and it started drizzling.
"It was the weather we kind of played in the first day, so made sure to stay warm and to take it a shot at a time."
Korda said throughout her five-win run that staying in the present was the key to her success, and on Saturday she credited caddie Jason McDede with helping keep her in the moment.
"So that's our mentality, has been our mentality for the last couple years. Obviously there are weeks that you can do it much easier than others.
"When you're in the flow everything seems to click in a sense."
Green surged up the leaderboard with a round that she said "felt very easy."
"I hit 17 greens and missed a few fairways, but actually hit it really close," she said. "So it was really nice to actually not have to stress about trying to make pars today."
After picking up birdies at the third sixth and seventh, Green added six more on the back nine, including three in a row at the 15th, 16th and 17th.
"It did feel like autopilot for a little bit there, which is very nice," she said after breaking the 18-hole tournament scoring record.
Green has two titles already in 2024, at the HSBC Women's World Championship in Singapore and in a successful title defense at the LA Championship at Wilshire Country Club.
"I feel like I've been able to glue things together," she said. "Last week I couldn't keep up with the girls. On the greens is kind of where I lost a lot of shots.
"Today I hit it close enough to be able to hole putts, which was nice. Didn't actually hole anything longer than 15 feet, so hitting it very well, so that was very nice."
Another Aussie, Gabriela Ruffels, carded a 68 to share third on 206 with Japan's Ayaka Furue, who posted a 67.
Overnight leader Atthaya Thitikul of Thailand posted a two-over 74 that left her tied for 15th on 209.
