Snedeker opened with a nine-hole record of 9-under 27 and carded two more birdies to tie the Torrey Pines North Course record of 11-under-par 61 and lead by two stroke after one round.
Charlie Wi is two off the lead after opening with a 63. John Senden and Jeff Quinney share third at minus-8.
Play for the first two rounds is spread over the North and South Courses at Torrey Pines. The South Course yielded few good scores Thursday as just one of the top-33 players on the leaderboard played there.
Woods, who has won his last six PGA TOUR starts, started on the North Course's 10th tee. He stumbled to back-to-back bogeys from the 11th, but responded with three straight birdies from the 14th to move into red figures.
The reigning British Open and PGA Championship winner hit the stick with his approach at the par-5 18th and the ball settled within 6 feet of the hole. He knocked the eagle putt in to make the turn at minus-3.
Woods birdied the second to get to 4 under. After six pars in a row, Woods drained a 7-foot eagle putt on the par-5ninth to close his 66.
'I didn't get off to the best of starts. I was going the wrong way and saw all the good scores being posted so I tried to get back to even-par as quick as possible,' Woods admitted. 'I thought I drove it really consistent all day, a couple loose iron shots here and there, but once I got my speed on the greens and got adjusted to the speed, I was able to make some putts.'
Snedeker flew out of the gate with four straight birdies, the first three of which were all inside 10 feet. That run was stopped when he eagled the par-5 14th.
The 26-year-old remained hot. He punched out from under a tree to 3 feet on 15 for another birdie and he came right back with a three-footer for birdie on 16, getting him to 8 under through seven holes.
After parring the par-3 17th, Snedeker rolled in a 4-foot birdie putt on the 18th to turn in minus-9. With that, thoughts of shooting 59 starting entering Snedeker's head.
'Probably when I made the turn. I was 9 under through nine,' said Snedeker, of the possibility of shooting 59. 'I tried to tee my ball up on 10 and it didn't want to stay up there my hand was shaking so much.'
Snedeker two-putted for birdie on the par-5 first to continue his roll. He finally cooled off as he two-putted for par on each of the next seven holes. Snedeker closed with a 10-foot birdie putt at the ninth, his last, to tie the course record.
'It was a great day. I played awesome,' said Snedeker. 'I kind of leaked a little oil coming in. I didn't get to where I wanted to be, but it was still a great round of golf.'
Wi, like Woods and Snedeker, played the back nine of the North Course first. He collected five birdies and a bogey to turn in 4 under.
The South Korean eagled the par-5 first, then dropped in back-to-back birdie efforts from the fifth to move to minus-8. Wi closed with a birdie on the ninth to end two behind Snedeker.
'I started on the back nine and I turned at 4 under, and I thought I was playing very well until I got to the 11th tee and learned that Brandt was 10 under after 10. I thought maybe it wasn't so good,' admitted Wi. 'I hit my irons really well today and I was able to make some putts. That was the difference between when I missed the cut in Hawaii and today.'
Two-time Masters champion Jose Maria Olazabal leads a group of nine players tied for fifth at 7-under-par 65. He stands alongside Robert Garrigus, Cliff Kresge, Darron Stiles, Kevin Sutherland, Johnson Wagner, Steve Marino, Gavin Coles and Chris Couch.
Woods is one of 10 players tied for 14th at minus-6. Among the others shooting 66 Thursday were amateur Jamie Lovemark and former world No. 1 David Duval.
Two-time winner Phil Mickelson struggled to an opening round 2-over-par 74 on the South Course.