Woods holed a 28-foot putt for eagle at the 18th to sign for a 5-under 65 and share the lead alongside fellow American Rickie Fowler.
The pair are one ahead of Gary Woodland and Justin Rose with Rory McIlroy, Justin Thomas and Tony Finau T5 at 3-under.
Day posted a 2-under 68 to be one of four players sharing eighth, the best of the three Australians in the field by two shots.
Cameron Smith mixed four birdies with four bogeys for an even par 70 and T16 while Marc Leishman continued to struggle with his game on his way to a 73 and T28 in the 30-man field.
But as it has been for much of 2018, it was all eyes on Tiger Woods at the season’s big finale, the 14-time major winner overcoming a bogey at the opening hole with two front nine birdies to turn 1-under.
It was the back nine however, where he produced the fireworks with birdies at the 12th and 14th followed by his final hole heroics.
“This putt was taking forever for the grain to take it,” he said of his last shot of the day. “And it finally did in the last three or four feet.”
Woods’ 2018 comeback has been a remarkable story with just two missed cuts in 17 appearances.
The 42-year-old has amassed six top-10 results on his resume and two of those in major championships with a T6 at The Open and outright second at the PGA.
“My body has gotten better,” he said of how he felt the year had unfolded.
“My doctor said it’s going to take you a while to get your body back and get everything moving again, and it’s taken a little time. Meanwhile, trying to figure out not only my swing changes but equipment and trying to hit a moving target with my game.
“Everything has evolved. I feel completely different than I did at the beginning of the year. The shots are similar, but they’re done differently.”
While there is a lot of golf yet to be played this week, the leaderboard shows Woods projected to finish second in the FedEx Cup if all players were to maintain their current positions in the field.
That is an extraordinary achievement for a man whose on and off course struggles since 2009 have been well documented.
“This is one of those where you’re not going to get an exemption into this event,” he said of the sense of pride in qualifying for the 30-man Tour Championship.
“You have to earn it and be part of the top 30, consistent and one of the guys who’s had a good year.
“I’ve earned my way back. All things considered it’s been a pretty huge success.”
FedEx Cup leader Bryson DeChambeau, who has won two of the first three playoff events, endured a roller coaster day and while he eventually posted 1-over, it could easily have been worse.
A disastrous front nine featured two double bogeys and a bogey against just one birdie and at 4-over he was at the tail of the field.
But the unorthodox Californian impressed on the back nine, regaining his composure and posting three birdies to get to 1-over and, while less than pleased to be T21 in a 30-player field, will take some confidence from his finish.
SIGNATURE HOLES - 16TH AT SANCTUARY COVE PALMS COURSE, QUEENSLAND:
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