PGA champion Justin Thomas (65) and Webb Simpson (66) were a stroke behind with Britain's Tommy Fleetwood (67) and American Jamie Lovemark (68) another shot adrift.
Sweden's Alex Noren also was in the mix as he bounced back from a 75 to shoot 65, a closing eagle boosting him to four-under at 206.
Woods, making his third start of the PGA Tour season after a year-long absence following back surgery, birdied his final hole for his first round in the 60s in nearly three years.
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He was tied for 11th at even par 210 despite two late bogeys.
"Even though I shot 69, it was probably the highest score I could have shot today," the 14 times major champion told CBS Sports. "I really hit it good.
"At least I put myself there where I have a shot going into tomorrow."
Woods gave himself plenty of opportunities for birdies, but made only three at the eighth, 13th and last holes.
"The hard part has been trying to get the ball to go into the hole," he said. "These greens are a little tricky."
The former world number one again had trouble at 15, making bogey after a double-bogey on Friday. He also dropped a shot at 17 with another bogey before the par putt at 18.
"You never know what can happen the last few holes here," said Woods, knowing he will need another sub-par round on Sunday to be a factor.
Thomas will be aiming for his eight PGA Tour victory after making four of his six birdies on the back nine for his strong finish.
Simpson, whose biggest win came at the 2012 U.S. Open, had an impressive start, going out in three under before adding a fourth birdie on the 13th.
Eagles at the fourth and last holes highlighted Fleetwood's day with the first coming from 140 yards.
Lovemark, Friday's co-leader, dropped from four-under to minus two with a troublesome double bogey at 15.
(Reporting by Gene Cherry in Salvo, North Carolina; Editing by Greg Stutchbury)
