World No. 1 Justin Rose shot a six-under-par 66 to open up a three-stroke lead at the Farmers Insurance Open in San Diego on Friday.

While Tiger Woods posted his second consecutive 70 to slip 11 strokes off the pace, Rose excelled on the Torrey Pines south course to sit at the top of the leaderboard on 15-under 129, matching the best 36-hole score for a PGA Tour event at the venue.

Hideki Matsuyama showed signs of life after a recent period in the doldrums, matching Rose's 66 on the south course to jump into second place on 12-under.

Matsuyama was ranked No. 2 two less than 18 months ago but has slipped to 33rd.

Spanish overnight leader Jon Rahm battled to a 72 on the south to slip five strokes behind Rose, equal third with Americans Billy Horschel (68) and Ryan Palmer (67).

Northern Irishman Rory McIlroy shot the day's lowest score, a 65 on the easier north course, to move within seven shots.

"My drives were a lot more stable than the first day, so I was able to play comfortably. It was really nice getting two in on approach," Matsuyama said.

"I think I'm getting nervous since I haven't won a tournament in a long time, but I want to put (that feeling) to rest."

Satoshi Kodaira missed the cut at 2-over after shooting a 74.