In the fourth round in Alabama, Dryburgh produced a brilliant seven-under 65 at Magnolia Grove in Mobile to make a significant leap up the leaderboard as he moved into joint-11th on nine-under.
Davidson, who now flies the Australian flag, is on the same total after she signed for a 69, which started with a bogey but was then followed by four birdies.
Players finishing in the top 45 and ties at the end of 144 holes will receive 2022 LPGA Tour status.
“Very happy with how the week has gone,” said Dryburgh after producing one of the best rounds of the day as she carded eight birdies, including five in six holes on the front nine.
“I have played really well this week but hardly made any putts the first three rounds so it was nice to get a good run of birdies going today. It gives me a lot of confidence for this week.”
After getting a chance to recharge the batteries, the 74 players still standing will resume the battle for cards on Thursday.
“ I’m planning to take Monday off and then play nine holes on Tuesday and Wednesday,” said Dryburgh, who has held a status for the LPGA Tour over the past few years.
“I was able to play a mini tour event on these courses a couple of weeks ago, so I have played the courses before which is helpful.”
French player Pauline Roussin-Bouchard leads on 19-under, two ahead of Korea’s Hye-Jin Choi, with newly-crowned LET No 1 Atthaya Thitikul and Australian Stephanie Kyriacou both handily-placed on 13-under.
Kyriacou made her move by shooting the round of the week in the fourth circuit, carding seven birdies and an eagle for a nine-under 63.
“I think everything just clicked,” said Kyriacou, who turned professional after winning the LET’s 2020 Australian Ladies Classic Bonville as a 19-year-old amateur.
“Over the last couple days some things were working and some things weren't, and then today they just both were in sync.”
England’s Meghan MacLaren is also still in the hunt, sitting joint-39th.