It matched his best score of the year, a four-under 66 in the opening round of the Greenbrier Classic earlier this month, but was the lowest with regard to par during his 2015 campaign.
Woods, the tournament host, birdied six of his last 13 holes to rocket into contention with an eight-under total of 134, his final birdie of the day coming at the par-five eighth where he drained a 35-footer before celebrating in roundhouse style.
"I feel like I can still compete, I feel like I can still win," the former world number one told reporters after mixing six birdies with a lone bogey at the par-five 14th, his fifth hole of the day, to finish one stroke off the early lead.
"A year-and-a-half ago, I won five times ... so it's not that long ago that I was player of the year. I know now my ranking's awful but it's a matter of I was away from the game for a long period of time, plus playing poorly compounded it.
"I just need to keep playing and keep plugging along and eventually I'll come back up (the rankings)."
Woods, whose world ranking has plummeted to a mind-boggling 266th, has recorded three missed cuts, a withdrawal and one top-25 finish in eight starts on the 2014-15 PGA Tour.
He shot his worst round as a professional, an 85 at the Memorial tournament last month, and has since missed the cut at the U.S. Open and British Open -- the first time in his career he has done so at consecutive major championships.
"I have been through this before," said the 39-year-old American. "You make changes to the game, it takes a little time sometimes. You've just got to be patient with it."
Asked how it felt being back in contention heading into the weekend, Woods replied: "I'm in a good spot. I'm looking forward to the weekend and I'm looking forward to getting after it."
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)
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