The 42-year-old bounced back to birdie the par-five 18th and join Rose at the top of the leaderboard, with Rory McIlroy two shots off the lead on five under and Jon Rahm, Justin Thomas, Patrick Cantlay and Billy Horschel a shot further back.
Woods, whose last win came in the 2013 WGC Bridgestone Invitational, told Sky Sports: 'I ground out a round today, I wasn't as sharp as I was yesterday and missed a few shots but hung in there with a bunch of pars and made a couple of putts which was nice'.
"The best way to describe today is I ground out a round", said Woods, a former two-time victor of the season-ending tournament.
He began the round tied at the top with American compatriot Rickie Fowler but soon moved two clear of Fowler who bogeyed the first hole.
The closest he was in any of the other chances was four shots, at both The Open and the PGA Championship, the latter where he shot a final-round 64 and finished two shots back of Brooks Koepka. The world No. 1 then hit a disappointing chip to 11 feet, and two-putted for an opening bogey. When Rose birdied the hole, the advantage was down to three strokes.
When Woods was in his prime, it was typical to see his playing partner crumble over the weekend, but Rose has managed to hold his own playing with Tiger in the past.
"This course, the way it's playing right now, you've got to be so patient, " Woods said.
Woods says staying calm under pressure will be key in order for him to shoot low scores over the next two rounds.
"We don't play very many places like this where if you have control of your ball, if you have control of your game, you're probably going to have a good chance to win, " Thomas said.
Everyone loves a victor - even if this one hasn't won a PGA Tour event in five years.
His second round was a sour mix of just two birdies and seven bogeys.
The most recent sports headlines delivered to your inbox every morning.