The world number one trails overnight leader Miguel Angel Jimenez by one shot after battling his way to a level-par 71 on Friday to finish on two under, one behind Spaniard Jimenez.
Woods was level with Briton Lee Westwood, Sweden's Henrik Stenson and fellow American Dustin Johnson after sinking a birdie on the last hole to end an attritional second round with a flourish.
"Just got to continue plodding along. Just continue just being patient, putting the ball in the right spots and trying," Woods said.
"We're not going to get a lot of opportunities out there, but when I have, I've been able to capitalise, and hopefully I can continue doing that."
Jimenez added a 71 to his opening 68 to top a congested leaderboard.
"I feel relaxed," he told reporters. "And I tell you, I love what I'm doing. I play golf. I do this for a living. And I've keep doing the same thing for 25 years."
Westwood, bidding for his first major title, made six birdies in the first 12 holes of his second round before three bogeys stalled his progress.
"I felt pretty comfortable," he said. "I was hitting the ball well. Putting nicely. The golf course got really difficult. The finish is tough. 16, 17, 18 are playing hard. So it's like most major championships, it's a grind out there."
Briton Martin Laird, Argentina's Angel Cabrera, American Zach Johnson and Spain's Rafael Cabrera-Bello will start the third round at one under par.
(Reporting by Ed Osmond, editing by Martyn Herman)
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