The eagle came after a ridiculous approach on the par-5 18th. 126-200 in the PGA Tour's FedEx Cup standings, and Paisley and other non-members with enough money to have placed in the top 200.
Woods already considers this a successful year just by making into the 30-man field at East Lake for the FedEx Cup finale, where everyone has a mathematical shot at capturing the $10 million bonus.
After starting off with a birdie, Finau made back-to-back bogeys at holes 4 and 5.
Woods, who will represent the United States at next week's Ryder Cup, recovered from a bogey at the first and made back-to-back birdies at five and six.
The 25-year is projected to drop to No 3 in the final standings.
While the rankings formulas continued to play out, Fowler and Woods were the stories on the course Thursday.
The 65 was Fowler's fourth in five rounds since coming back from an oblique injury following the PGA Championship at Bellerive.
Rose, who is playing his first tournament since becoming world number one, won the European Tour's equivalent Order of Merit in 2007. "I chipped and putted a lot, so my short game feels pretty good". This is the second straight tournament in which he has bolted out to the first-round lead.
Woods, who has not featured in the season-ending Tour Championship since 2013, told Sky Sports: "After the three-wiggle at one, I played my way back into it and hung in there and made two good putts at five and six that basically turned the whole round around".
A day after opening with a course-record equalling 62 at Aronimink Golf Club and sharing the lead, Woods stalled during an even-par 70 that left him at eight- under-par and five shots off the pace. "Conditions were soft there".
"The only hard part was getting my speed on the greens early".
"It was just unfortunate I just didn't keep it going". If you drive the ball in the rough, you know you can't get the ball close.
"So it puts a premium on driving, and it puts a premium on allowing for a little bit of chase on some of these greens". I'd like to see that happen, I just need to go out there and do it.
Now, it's about putting all aspects of his game together over a four-day stretch - or even a three-day stretch at next week's Ryder Cup in France.