In his first start since a tie for 22nd at The Masters, Woods had eight birdies on his way to a 6-under-par 66 on the demanding Hollow Quail course.
Woods stood at 9-under 135 after 36 holes.
Arron Oberholser (68), Notah Begay (70) and first-round leader Kirk Triplett (73) shared second at 7-under 137. Vijay Singh, winner of the last two PGA Tour stops, shot a 70 and was tied for fifth at 138.
Woods one-putted 12 times and holed out from off the green once, needing just 22 putts in all. But he suffered a disappointing bogey at the par-5 15th, where he put his tee shot into the water.