Sweden’s Stenson, who played in the final group with Woods, birdied the last hole Thursday in a round that included seven birdies and one bogey at the East Lake Golf Club.
Stenson started quickly with five birdies in a six-hole stretch from the second to grab the lead in the final tournament of the PGA Tour’s playoff series.
His hot streak consisted of just two putts from outside five feet as he stuck the majority of his iron shots close to the pin.
“That stretch between one and seven I guess is as good as I’ve ever hit it in a round of golf,” said Stenson, who tied his career low nine-hole score with a 30.
Stenson, who won the Deutsche Bank Championship earlier this month, can capture the FedEx Cup if he can hang on to his lead for the rest of the tournament.
Stenson’s playing partner Woods was the only golfer not to post a birdie in the first round.
The American struggled to a three-over 73 which put him 29th out of 30 players. The only player to shoot a worse score was PGA Championship winner Jason Dufner, who had 74.
Australia’s Adam Scott is in sole possession of second place following his five-under 65, while Americans Steve Stricker and Billy Horschel share third at four-under 66.
Roberto Castro shot a 67 to sit alone in fifth.
Reigning FedEx Cup winner Brandt Snedeker had a one-under 69 and is in a tie for 14th place.
Horschel parred his final four holes to hold the clubhouse lead for a while.
“It all comes down to putting the ball in the fairway. I think if you’re in the rough it’s hard to judge whether it’s going to come out flying or it’s going to come out dead and you can’t control the spin,” said Horschel.
“I did a good job putting the ball in the fairway, which gave me an opportunity to attack the flag.”
Playing in the penultimate group ahead of Stenson, Scott stormed up the leaderboard with a sizzling back nine.
The Masters champion countered bogeys at the third and eighth with a birdie at the sixth to make the turn at one-over, then poured in six birdies over a seven-hole stretch from the 10th to grab a share of the lead.
“This is always a tricky course,” Scott said. “If you’re playing well, there’s a good chance to score and if you’re playing bad it’s really tough to score out there.”