Woods shot a 7-under 65 over the Torrey Pines North Course during a steady, light rain and stood at 11-under 133 for 36 holes. He has won seven times at Torrey Pines, a collection of victories that has included the 2008 U.S. Open.
Friday's round was highlighted by an eagle at the par-5 18th. He suffered a lone bogey at the par-4 eighth when he drove into a fairway bunker.
Alone in second at 135 was Billy Horschel, who is in his third year on the PGA Tour and is seeking his first victory on the circuit. Horschel shot a 3-under 69 on the South Course, the harder of the two being used for this week's event.
Those who survived the 36-hole cut will play the final two rounds on the South Course.
Nick Watney was among those at 137 in a tie for ninth. Phil Mickelson bogeyed the final two holes to shoot a 71 and barely made the cut at 1-under 143. Tournament of Champions winner Dustin Johnson will also play on the weekend after finishing 36 holes at 141.
Woods climbed from No. 50 in the world to No. 2 last year thanks to three victories. He opened his 2013 season by missing the cut on the European Tour last week, but so did world No. 1 Rory McIlroy.