Ko carded a near flawless third round 66 to sit at seven under and fourth overall, with a double bogey on the 13th hole the only blemish on her scorecard.
Germany's Sophia Popov blistered the front nine, and raced out to an opening-round lead at the Pelican Women's Championship on Thursday at Belleair, Fla.
The 27-year-old Kim is the first player to follow her first major victory with a win in her next start since Ariya Jutanugarn in 2016 in the Women's British Open and CP Women's Open.
Ally McDonald, playing alongside Popov and Ko in an afternoon threesome, was at 67 with Womens PGA champion Sei Young Kim, the No. 2 player in the world.
"Once we got to a point, I just tried to take Sei Young out of it and play like a little tournament within the rest of the field", McDonald said.
Kim had an 8-under 132 total in the first-year tournament originally set for the same week as the PGA Championship in May. I'm really happy with how I played. I made some good putts coming down. "That is way to make more birdies". "The way it usually happens is that you're not thinking, and I think that's what was happening", she said of her 29.
A bogey in the eighth, however, pushed her back to even and on 3-over in aggregate after nine holes.
McDonald started a run of her own on the back nine, but then dropped a shot with a bogey on 16.
"I just gave myself better numbers, and with the wind it's kind of tough to get yourself exactly the numbers that you like".
Popov bagged six birdies on her first nine holes, including five in a row to end the front nine, on her way to a 6-under-par 64 for the lead in the inaugural event.
That saw her slip from third spot to a three-way tie for sixth and threatened to hamper her progress, but she responded in strong fashion, with a birdie at the next hole, as well as at 17 and 18, adding to her three earlier in the round.
She skipped her title defence at the pandemic-delayed ANA Inspiration in September, and is returning to the LPGA tour for the first time in nearly a year.