The American, who has been stuck on 14 Majors for five years, lashed his opening tee shot into heavy rough via perhaps the only tree on the course.
He found an unplayable lie and had to take a drop as it looked as if he would struggle, but found his game and produced a run of four birdies after the turn to put himself in contention at sun-baked Muirfield.
Woods had a frustrating front nine, missing a couple of birdie chances, but struck at the 10th, 11th, 13th and 17th to complete a satisfactory start on the lightning-fast links.
His only birdie going out was on the par-three fourth where he tickled in a slippery eight-foot putt.
Woods went out in one-over 37 after bogeying the sixth by duffing a chip and watching his ball roll back off the green.
But then came the back nine, in which Woods played superb golf in some of the most difficult conditions of the day.
As the world number struggled early on, three-times Open champion Nick Faldo said he believed that Woods might never lift the Claret Jug again in his career.
Faldo was speaking after he shot an eight-over 79 in the first round at Muirfield, venue for two of his three Open triumphs, in his first competitive round for three years.
"I think it may be difficult for Tiger now," Faldo said. "Perhaps there is too much happening for him.
"All the stuff that went on off the course and his injury problems. Tiger used to be able to make things happen on the course and he has struggled to do that recently," added Faldo.
"He has issues with his swing, look at what happened to him today on the first tee? He snap-hooked the ball. That tells me something is not right."
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