Rose turned in the top score of the day, a 7-under 65 and was able to ousthoot defending champion Woods, who finished with a 3-under 69.
Bill Haas steadily climbed the leaderboard after an afternoon start and recorded two birdies and an eagle on the front nine. But two bogeys on the final two holes would put Haas at 3-under-par and in a tie for fifth place.
Only John Huh, with a 5-under 67, and John Rollins, with a 4-under 68, finished their rounds within three strokes of Rose.
"I just sort of let the round evolve and hit it in the right places a lot of times and managed to make some putts," Rollins said.
Fan favorite Phil Mickelson finished his round missing a par putt on the 18th hole and ending up with a 1-over-par 73. Mickelson recorded seven bogeys on the day, but an eagle on the par-5 16th hole helped him finish close to even par.
Rose and Woods are scheduled to tee off tomorrow at 12:45 p.m. and Mickelson's group, including Sergio Garcia and Brandt Snedeker, will start its round at 8:05.