Kim wrapped up her round in dying light at Wildfire Golf Club, her 16-under par total of 200 giving her a two-shot lead over American Stacy Lewis.
The 19-year-old said every aspect of her game felt good.
“Been really good with the driver… totally all the clubs,” said Kim.
“If I miss, I save, so I’m playing good. All the putts feel good.”
After her only bogey of the day, at the par-four 13th, Kim birdied three in a row, capping the burst with a 25-foot birdie putt at the 16th.
Lewis had six birdies in her five-under 67 for 202, and was one stroke in front of fellow Americans Alison Lee and Kim Kaufman.
Lee rocketed up the leaderboard with a stellar nine-under par 63 that included nine birdies.
Kaufman, who had grabbed the halfway lead ahead of Kim when the second round was completed on Saturday morning, posted a third-round 70 for a 13-under total of 203.
World number one Lydia Ko of New Zealand headed a group on 204 after her second straight 69. She was joined by South Koreans Jang Ha-Na – who posted her third successive 68 – and Lee Mi-Hyang, who signed for a 68.
The tournament had been behind schedule since a four-hour weather delay on Thursday morning.
Sixty-six players had to complete their second rounds on Saturday morning, and it was a race against the desert sunset to complete the third round.