Stanley shot a 4-under 68 over the Torrey Pines South Course for a two-day total of 14-under 130. Brant Snedeker, who had a 64 over North Course, finished at 131.
Stanley, seeking his first PGA Tour victory, and a co-leader after the first round, suffered a double-bogey at the par-4 14th hole to spoil an otherwise solid round.
Sang-Moon Bae and Martin Flores, both hoping for a breakthrough week on the tour, shared third at 12-under 132. Both fired a 67 Friday on the South Course, the more difficult of the two used for this event.
Bae, a winner 11 times in Asia, earned a spot on the tour this season by surviving the PGA's qualifying tournament late last year. Flores gained his exemption by finishing 24th on last year's Nationwide Tour money list. The top 25 on that list made it onto the tour.
Spencer Levin, who shared the opening-round lead with Stanley, stumbled to a 76 on the South Course and slipped back into a tie for 20th at 138.
Phil Mickelson, who has won this event three times, missed the cut by three shots. He will be back in action next week when the tour moves to Scottsdale, Ariz.
All those who survived the cut will compete on the South Course over the final two rounds.