Scott made six birdies in seven holes for a 29 on the back nine.
"First seven holes is probably as good a proximity to the hotel as I've ever had," Stenson said. "Seven iron shots and made five birdies out of that."
There were birdies galore on a warm, relatively calm afternoon at East Lake except for Woods.
Woods missed a short birdie putt on his opening hole that set the tone for the day. He was the only player in the 30-man field to go without a birdie. On the par 5s, Woods three-putted for par on No. 9 and missed a putt just inside 10 feet on No. 15.
It was only the seventh time in his PGA Tour career and third time at East Lake that he went an entire round without a birdie. Woods shot a 73, matching his highest opening round of the year on the PGA Tour. He walked past reporters without comment.
Stenson, the No. 2 seed and the hottest player in golf over the last three months, and Scott (No. 3) only have to win the Tour Championship to capture the FedEx Cup and the $10 million prize.
Steve Stricker rallied late with three straight birdies for a 66, tied with Billy Horschel.
Stenson began his big run with four straight tournaments in the top 3 including two majors and a World Golf Championship and then won the Deutsche Bank Championship. But he was coming off a mediocre performance in the BMW Championship last week that left him so angry he smashed and broke his driver on the final hole, and then smashed up a locker at Conway Farms.
Plus, he was coping with a sore wrist from last weekend that hurt so much he only played nine holes this week in practice.
It was the latest example of the Swede's temper, and he handled it with an apology to Conway Farms and self-deprecating humor.
"I really knew I had to be in a good frame of mind coming out there if I wanted to play good golf this week," Stenson said. "As some of you noticed, I wasn't that on Monday when I finished up in Chicago. So it was a good turnaround mentally. I stayed very level-headed kept the head on, both myself and drivers and played a great round of golf."
Asked how he could go from the joy of winning a FedEx Cup playoff event to losing his temper in one tournament, Stenson replied, "I can tell you don't have much experience with Swedes, do you?"
"No, I'll tell you I've always been a bit of a hot-head, and I just haven't been able to get any rest," he said. "I was looking forward to that Monday back home and lying on the couch the kids in school and me just doing nothing, and I ended up playing golf again on that Monday. I was just tired, and I pushed myself over the edge there.
"That's not the best place to be and not the best frame of mind to play good golf," he said. "I'm really delighted with the change I made to today."
In his Tour Championship debut, his head was in the right place, his wrist felt fine and Stenson was on top of his game like never before. He had one stretch of three birdies all within 4 feet, capped off by a 6-iron from 207 yards over water to a right pin that settled a foot away.
And he did it all in the presence of Woods, the No. 1 player in the world.
"Normally, he's doing it to everyone else," Stenson said.
Seventeen players broke par in the opening round.
Woods wasn't alone in his struggles. Phil Mickelson switched to the claw grip midway through his round and nothing seemed to help. He had a 71. Nick Watney, coming off a runner-up finish in Chicago just to get into the Tour Championship, had a 72. PGA champion Jason Dufner was in last place at 74.
Scott also was angry at himself, only because he was giving himself so many chances off the tee and throwing them away with short irons in his hand. He was 1 over at the turn, but two great shots into No. 10 which plays as a par 5 for the members sent him on his way. His longest putt for those six birdies on the back nine was 12 feet, and Scott had to settle for a two-putt birdie from 10 feet on No. 15.
"It was a tale of two nines, there's no doubt," Scott said. "I missed three greens with wedges on the front nine and wasted all my chances to score. I hit two good shots into 10 and rolled a putt in, which calmed me down. And they I just went and played, and played the way I felt I could."
Henrik Stenson -6
Adam Scott -5
Billy Horschel -4
Steve Stricker -4
Roberto Castro -3
Phil Mickelson +1
Tiger Woods +3