Davis, who was third on 11 under par at the halfway stage, was five under for the second day in a row to be level with Bryce Molder at the top of the leaderboard.
The 35 year old, in a run of poor form heading into this million-dollar event, has not won on the US PGA Tour but will be aiming to keep his nerve in the final round after a bogey-free two days.
After an impressive 64, Zach Johnson is a shot off the leaders while first round joint leaders Jeff Overton and Jason Bohn, with 66 and 68 respectively, are alongside Ben Crane (64) at 14 under.
England's Paul Casey and Martin Laird of Scotland were in a group tied for 28th, at eight under, after strong rounds of 66.
K J Choi earlier came within one hole of an extraordinary third round before his day was ruined by a quadruple bogey at the 18th.
After seven birdies and an eagle, Choi was on target for an eight under round of 62 before he hit trouble on the final hole.
His tee shot went left, he found the water with his third, then skidded past the green with his sixth, before eventually putting from eight yards to sign for a 66.
A par on the last would have put him firmly in contention on 14 under for the weekend.