Woods found the green with his second shot into the par-five 18th and then brilliantly holed the near 30-foot putt in a round of a five-under par 65 to tie fellow American Rickie Fowler in heatwave conditions on the East Lake course.
Woods is now projected to jump 18 places and into second place on the FedEx Cup standings.
It is also the second straight event in succession at which Woods has shared the first-round lead after he and Rory McIlroy were tied at the top with 62s on day one of the BMW Championship in Philadelphia.
“To finish with an eagle was nice as I hammered that drive up the left side, and it was nice to see it not in the rough before hitting five-wood to the green,” said Woods.
“In order for me to get it there onto the green, I had to not have my five-wood kick up in the air, and so once it hit its peak, I knew it was good and I started walking after it, and it ended up on the green and I had a good look at eagle,” said Woods.
“It took forever for that putt to start breaking, grain coming down off the left. But once it snagged it, it was going straight right.”
Woods had began his round with a bogey but soon regrouped with birdies at the fifth and sixth holes and on a course where he claimed the FedEx Cup championship trophy in 2007 and 2009.
He then birdied the 12th and downhill 14th holes ahead of the eagle on 18 in a round that included just 28 putts.
“I played really well today and though it wasn’t exactly the start I was looking for in taking the bogey at one, I made two good putts there at five and six and got to under par, and then from there I hit it pretty good, made a few putts,” added Woods.
“But more than anything, I missed it all on the correct sides. Even the fairways I missed, all were on the correct sides. I had nice angles.
“The shots I missed were on the greens, all had beautiful angles. All in all, I had a lot of control today.”
Fowler capped his round with back-to-back birdies at five and six and while he dropped a shot on seven, the World No 9 birdied eight and then played the 11th to 18th holes in three under.
“It was a good day. I didn’t get off to necessarily a great start on my swing but I managed to kick my way around,” said Fowler.
“I think I missed one fairway, which the ball was in the first cut, and I think I hit every green from there on in. Made it very stress-free.”
World No 1 Justin Rose, who birdied his closing two holes in a score of 66 to be tied third, is projected to move up a place and also become No 1 in the FedEx Cup.
Current FedEx Cup leader Bryson DeChambeau had an East Lake debut he would rather forget in posting two double-bogeys over his opening nine en-route to a round of 71.
The 25-year is projected to drop to No 3 in the final standings.
PGA TOUR CHAMPIONSHIP
Course: East Lake GC. Yardage: 7,385. Par: 70.
Purse: $9million. Winner’s share: $1,620,000.