Korda only took advantage on two of the four par 5s at Mayakoba and had to scramble on the par-5 18th. But she had the right touch on a gap wedge from just over 50 yards to four feet to close out her round with a birdie.
That allowed her to catch Do (69), who finished with a bogey at the par-4 ninth.
They were at nine-under 135, having faced a stronger wind than the morning wave from the day before on the course along the coast of the Caribbean Sea.
"Drive it straight, hit it close and make putts," Korda said of the key to playing El Camaleon, the rest course that previously hosted PGA Tour and LIV Golf events.
Melanie Green (70), who shared the 18-hole lead with Do, had a slow start until making three birdies over her last six holes to sit one shot behind, while Japan's Minami Katsu (69) is two shots adrift.
Gabriela Ruffels had a 72 and is the leading Australian at two under, while Robyn Choi (76) is one over and Hira Naveed (72) two over.
Compatriots Sarah Kemp (79) and Su-Hyun Oh (77) won't feature over the weekend after finishing the second round 10 and 14 over.
Korda hit only seven of the 14 fairways, but putted for birdie on all but two holes.
She also had a big following, only partially related to being the No.1 player in women's golf with her wire-to-wire victory last week in The Chevron Championship for her second win this year, and her third career major.
She was playing alongside Mexican Gaby Lopez (71), who is four shots behind.
"Playing with Gaby, the crowds have been amazing to see the local support for her," Korda said.
"And not complaining about where I am on the leaderboard. Playing some solid golf and playing in front of fun crowds ... Hopefully I can continue playing well, good golf going into the weekend."
Do, the 36-year-old American, managed her 69 without making birdie on the par 5s. But her iron game gave her plenty of good looks for birdie and she converted four of them.
She tied for ninth at the Riviera Maya Open a year ago, her only top 10 on the LPGA Tour.
With AAP.
