The former world number one carded a five-under 67 to end the third round on 11 under, four shots behind South Korea's Charlie Wi, who is chasing his first Callaway Men's RAZR X HL Hybrid/Irons - 3-4H, 5-PW
win.
Between them in second place is American Ken Duke on 12 under.
Two late bogeys saw Ireland's Padraig Harrington drop to eight under par for a share of ninth place.
Englishman Greg Owen is a shot further back.
Woods - taking part in the California event, which is played over three venues, for the first time in a decade - created a stir with his run of birdies on the Pebble Beach course. Callaway Men's RAZR X HL Hybrid/Irons - 3-4H, 5-PW
However, he had to settle for seven pars to end his round, denting his hopes of a first tour title in more than two years.
Wi was steady throughout his three-under-par round of 69 at Spyglass Hill, while Duke's five-under 65 at Monterey Peninsula was bettered only by compatriot Ryan Palmer's 64.
Although Phil Mickelson briefly threatened, he struggled on Pebble Beach's par fives to shoot a 70, leaving him six shots off the pace heading into the final round.