Johnson had an eagle on the par-5 fourth hole to cap a comeback, after starting on the back nine and slipping to even par for the round. She finished with a 2-under 71 in the sweltering heat at Chicago Golf Club.
Davies struggled early on the back nine with a double bogey at 11, and fell to even-par overall before four birdies in six holes put her back at the top of the leaderboard.
Juli Inkster is third at 1-under 145 after a 71. Danielle Ammaccapane fought back with a 71 after a rough first round and trails by four shots.
First-round leader Elaine Crosby trails by six strokes after shooting a 5-over 78.
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