Watched by huge galleries after teeing off at the 10th on the heavily tree-lined Spyglass Hill Golf Course, the former world No. 1 mixed six birdies with two bogeys to end the day five strokes off the pace.
Woods, back at the pro-am celebrity event for the first time in a decade and hunting his first victory on the PGA Tour in more than two years, evoked memories of his glory days.
He was in sparkling form off the tee, a little frustrated by his approach play and could have been at least two or three shots better had a few well-struck putts not halted inches short of the cup or slipped past the edge.
"I drove it great, I had it on a string for most of the day," Woods told reporters after hitting 11 of 14 fairways and 15 of 18 greens in regulation on the most difficult of the three venues hosting this week's event.
"I just wasn't very good with my irons so I'll have to go and work on that. I left a few putts out there ... and I didn't give myself enough looks when I had wedges in my hand."
With barely a breath of wind on the picturesque Monterey Peninsula, scoring conditions were near-perfect and Woods knew it was crucial not to end the first round too far adrift.
"When the scores are like this, I can't get too far behind the lead," said the 36-year-old American. "Hopefully tomorrow I can get it going over there at Monterey. It will be an important day to put it together and make some birdies."
Woods made a sizzling start with consecutive birdies, hitting a superb approach to three feet at the par-four 10th and narrowly missing an eagle putt from 14 feet at the par-five 11th.
The 14-times major winner made his first mistake of the day at the par-four 13th where he pulled his tee shot into the left fairway bunker. From an awkward stance, Woods failed to reach the green in two and ended up with a bogey.
After comfortably parring the next three holes, he picked up another shot at the par-four 17th where his approach shot pitched beyond the cup and spun back to within 10 feet.
Another par followed at the 18th for Woods to enter his back nine at two under.
He picked up further shots at the first and third, where he sank a 25-footer, before bogeying the par-four fourth after his approach flew the green.
However, Woods rammed in a 15-footer to birdie the par-five seventh and parred the last two holes to remain at four under.
Though he has not won on the PGA Tour since the 2009 BMW Championship, he arrived at Pebble Beach this week with high hopes following his form over the last two months.
In his last three stroke-play events, Woods finished third at the Australian Open in November, won the limited-field Chevron World Challenge which he hosts in December and tied for third at last month's Abu Dhabi HSBC Golf Championship.
"I don't know if it's a good sign or a bad sign," Woods said of his 68, the fourth-best round of the day at Spyglass Hill. "With the scores the way they are, I thought I could have it lower than I did.
"I figured par today was going to be about 67 out here ... so I'm not too far away from posting a good number out here." (Editing by Frank Pingue and Peter Rutherford)