THOUSAND OAKS, December 7, 2013 (AFP) - The world number one, who started the day four shots off the lead, had 10 birdies and no bogeys for an 11-under total of 133.
That gave him a two-shot lead over first-round leader Zach Johnson, who had four birdies in a four-under 68 for 135.
"It was good today," said Woods, who has won this 18-man tournament he hosts for the benefit of his charitable foundation five times. He set the course record of 62 in the second round in 2007, en route to one of those triumphs.
"I only made probably two putts that were downhill. I hit a lot of good shots, leaving myself in these spots so my putts weren't really that difficult to make."
Woods saw a long putt at the seventh curl around the hole and drop in the back for birdie.
He kept his momentum with a key two-putt par at the par-three 12th and birdied 13 despite a tough lie in a bunker with an acorn behind his ball.
Oddly enough, Woods wasn't feeling that great as he warmed up for a round that was delayed for an hour by morning frost.
"I did not warm up well," he said. "I was not hitting it very good on the range."
He opened with back-to-back birdies at the first and second, leaving himself a putt of less than two feet at the first.
But it wasn't until the third hole, he said, that he felt his swing really click.
"I tried to keep that feeling the rest of the day, and I did," he said. "I hit a lot of good shots after that."
Woods' score was one shot off the best of his career. He has shot 61 four times, most recently in the second round of the WGC Bridgestone at Firestone in August -- where he went on to win by seven strokes.
"This is similar to what I did at Firestone this year," he said. "I think Firestone is a much more difficult golf course than Sherwood, but as far as quality ball-striking, I hit it equally as good today if not better."
American Matt Kuchar carded a 68 for 136 to stand alone in third place heading into a weekend that could see rain move across the rolling countryside course, 64 kilometres (40 miles) west of Los Angeles.
"The next couple days, if the weatherman actually does get it right, we are going to have a hell of a test," Woods said.
Johnson birdied the 18th to narrow the gap to Woods -- an especially pleasing finish after his bogey there on Thursday.
"Steady golf," he said of his round. "Four-under is a nice score. Amazing what Tiger did out there. It's just some incredible golf."
Former world number one Rory McIlroy, who captured his first win of 2013 just last week at the Australian Open, endured another tough day.
He carded a five-over 77 that included a double-bogey six at the par-four fourth and a quadruple-bogey nine at the par-five 16th.
Scores on Friday in the second round of the $3.5 million Northwestern Mutual World Challenge hosted by Tiger Woods (USA unless noted, par-72):
133 - Tiger Woods 71-62
135 - Zach Johnson 67-68
136 - Matt Kuchar 68-68
139 - Graeme McDowell (NIR) 72-67
140 - Bubba Watson 70-70
141 - Bill Haas 73-68, Jim Furyk 72-69
143 - Keegan Bradley 75-68, Ian Poulter (ENG) 76-67
144 - Jason Day (AUS) 76-68, Webb Simpson 73-71
145 - Jason Dufner 74-71
149 - Jordan Spieth 77-72, Steve Stricker 75-74, Lee Westwood (ENG) 74-75
150 - Rory McIlroy (NIR) 73-77, Hunter Mahan 70-80
153 - Dustin Johnson 74-79