In pursuit of his sixth victory this year, the American world number one drove the ball well but was not as sharp with his irons and his putting as he finished up four strokes behind the pace-setting Zach Johnson in an elite field of 18.
Woods, who has won his event a record five times, missed a three-footer for par on his opening hole and a birdie putt from a similar distance at the par-four last to end the opening round with just four players ahead of him.
"I felt like I hit the ball decent today," the 14-times Major champion said after missing only two fairways at Sherwood Country Club with a new driver in his bag. "I missed two short ones (putts) there at one and the kick-in at 18.
"That's a couple of shots right there, and I'm only two back. I had a couple of good ones (shots) on the back nine today that ended up in some very interesting spots. The golf course is kind of set up that way right now.
"There are some tough pins out there. You miss them on the wrong spots, you're going to pay a price and I think that's kind of what's signified in the scoring. No one is running away with it. Nobody went low today."
Only four players in the field dipped under par on Thursday - Johnson (67), Matt Kuchar (68), Hunter Mahan (70) and Bubba Watson (70).
Woods, who triumphed a season-high five times on the 2013 US PGA Tour, was making his first tournament appearance since tying for third at the European Tour's Turkish Airlines Open a month ago.
"Probably just my feel," he said of the hardest thing to regain in his game after a lengthy break from competition. "I drove it pretty good today, and I just didn't quite hit my irons well and didn't make a lot of putts.
"You've got to give these greens a little bit of respect. If you miss the ball in the wrong spots, which I did a couple of times above the hole, you have to play pretty defensively. I had a lot of putts where I had to worry about the speed."
Woods, who became the first player of black heritage to win the Masters in 1997, paid tribute to former South African President Nelson Mandela, who died earlier on Thursday at the age of 95 after a prolonged lung infection.
"I got a chance to meet with him back in '98 with my father (Earl) at his home and we had a great lunch together," Woods said, referring to a trip he made to South Africa that year to compete in the Million Dollar Challenge.
"It was one of the most inspiring times I've ever had in my life. He certainly had an impact on my life and certainly my father's. When he came out (of prison), the country (South Africa) could have fallen apart.
"It could have gone a lot of different ways, and he led it to where it's at now. The world is going to miss him."