American amateur Farah O’Keefe also posted a bogey-free 69 to move to seven under, putting her in a tie for third with compatriot Ryann O’Toole and South Korea’s Ina Yoon.
Korda has started the year in good form having won the season-opening Hilton Grand Vacations Tournament of Champions before claiming three straight runner-up finishes.
She won this event in 2024 at The Club at Carlton Woods, which is also in Houston, while 26-year-old Tavatanakit won in 2021 in California, when the event was named the ANA Inspiration.
The world number 66 said: “Chasing, leading, whatever – I feel like I’m just glad I have this opportunity to be in the mix.”
Her compatriot Jeeno Thitikul will not feature this weekend as the world number one bogeyed two of her last five holes to miss the cut by one stroke.
England’s Mimi Rhodes also missed out after following up Thursday’s round of three-under with a six-over 78, carding three bogeys and a double-bogey in her last five holes.