With the temperature gauge topping 100 degrees late in the day, Henderson’s red-hot display matched the conditions as she tied the front nine record at Mission Hills, covered in just 30 shots.
Korda, the sole leader for the opening two rounds, recovered from dropping three shots in two holes on her front nine with birdies at the 11th, 12th and 15th to join Henderson in the clubhouse on 12-under 204.
Henderson, chasing her second major crown and 10th LPGA Tour win, had started the day six back and only a bogey on the 13th prevented her from claiming the sole lead.
“Being a major championship, you’ve really got to stay patient and know bogeys are going to happen,” she told reporters.
Korda, chasing her first major, said she was “very proud” of the way she fought back on the back nine to match Henderson.
Playing in the last group, Korda was on course during the hottest part of the day, sheltering under an umbrella to find shade under the strengthening California desert sun.
Aussie veteran Katherine Kirk, who is in a three-strong chasing group two shots adrift of the leaders after a 67, summed up the feelings of many when she said she would like to win the ANA Inspiration and then perform the now traditional plunge into Poppie’s Pond, the water surrounding the 18th green.
“It’s so stinking hot out here and it would be great to cool off,” Kirk said.
Home hope Lexi Thompson, who famously jumped into the water after her 2014 victory, is tied with Kirk in joint third alongside South Korean Mirim Lee.
Thompson looked set to challenge the leading duo when she started with three birdies in the first five holes, but two later bogeys halted her move and she had to settle for a three-under 69.
With 10 players separated by just four shots at the top of the leaderboard, an exciting final round is in prospect, with Spain’s Carlota Ciganda on nine-under, one shot ahead of a group that includes another former Mission Hills winner, Stacy Lewis, and US Women’s Amateur champion Rose Zhang.