The 22-year-old American coolly drilled a six-foot putt on the par-5 18th for her seventh birdie of the day to card her lowest ever round at the tournament at Mission Hills Country Club. Her lone bogey came on the par-four fourth.
Korda leads by one from two-time major winner Chun In-gee of South Korea and Madelene Sagstrom of Sweden, who fired matching five-under par 67s.
Korda said a new practice routine has helped her build confidence with her short game as the three time winner on the LPGA Tour looks to make her major breakthrough.
“There was more work on the putting greens during practice round days,” she said.
“Even after my round or after my practice was done, I’d come out here and hit a few putts because at the end of the day golf is all about confidence.
“If I’m giving myself shorter par putts and not bombing my birdie putts by, it makes it a lot easier.”
The tournament is usually played in April but was pushed back due to the COVID-19 pandemic and is being held without fans in attendance.
The conditions are less than ideal at Rancho Mirage, with temperatures expected to soar above 100°F (37.8°C) during the tournament.
Nearby wildfires also impacted the air quality earlier in the week but the skies were clearer on Wednesday and Thursday. Reporting by Rory Carroll in Los Angeles; Editing by Toby Davis/Peter Rutherford