The world number one made five birdies over the par-70 Phoenix Country Club course after starting on the back nine, but his exploits were overshadowed by a red-hot Shingo Katayama of Japan, who heads the field after an opening 65.
Dropped shots at the 12th and seventh left Woods in a five-way tie for third with 2006 European Order of Merit winner Padraig Harrington and a trio of Japanese players.
Spain's Gonzalo Fernandez-Castano had nine birdies and five bogeys in an adventurous round of 66 to claim sole possession of second place in the southern Japanese resort of Miyazaki.
Woods had to apologise to Katayama after almost hitting him with a drive while the Japanese player lined up a putt on the 334-yard 13th hole.
"I didn't see the (warning) flags out on the fairway," a sheepish Woods smiled.
"So I hit. I thought they were off the green -- and they weren't. I apologised when I got up there."
The American's amazing run of six successive victories this season was ended by South Korean Yang Yong-eun at the Champions Tournament in Shanghai last week.
But Woods expressed his satisfaction with his start after making several mid-length putts for birdie or to scramble par in swirling conditions on the coast.
HANGING AROUND
"I basically just hung around," shrugged the 12-times major winner.
"I missed the ball in the right spots and made some nice saves to keep the round going. I was very pleased to shoot three-under today."
Katayama, sporting his trademark cowboy hat, drained a succession of lengthy putts in a superb round that evoked memories of his Dunlop Phoenix triumph six years ago.
"It doesn't matter if Tiger is playing or not," he said. "It's all the same to me. It's a wide open tournament, so I have to just try to keep the momentum going."
Katayama quickly forgave Woods for his indiscretion at the 13th, while playing partner Azuma Yano joked that he had wanted to pick up the ball and ask Woods to sign it for him.
Japan's Toshimitsu Izawa, Satoru Hirota and Hisayuki Sasaki all returned opening rounds of 67 to match Woods and Harrington.
Champions winner Yang, meanwhile, suffered a Shanghai hangover as he carded a four-over-par 74, along with two-times winner Thomas Bjorn of Denmark.
Britain's European Ryder Cup member David Howell also struggled, the Englishman slumping to a 77 to leave him in danger of missing the cut.
