Singh began the day a stroke behind Howell but offset his only bogey with four birdies and the eagle, reaching 9-under 201.
There have been three Tour Championships at East Lake and Singh has been the only 54-hole leader. He lost a playoff to Hal Sutton in 1998 and tied for third in 2000.
Singh was nursing a one-stroke edge before he sank his long, right-to-left breaker at the par-5 15th hole. The Fiji native was just trying to get the ball close and was stunned as it dropped.
"It was weird because where my ball was, that's where the pin was yesterday, and where the pin was, my ball was there yesterday," he said. "I three-putted. I said, 'Well, I knew the line, kind of.'"
Singh scrambled for pars on the final three holes, getting up-and-down from bunkers on the last two. The finish may have given him a lead comfortable enough for his 11th PGA Tour title.
"I'd just like to get off this year with a win," said Singh, who won in Houston earlier this season. "That's bigger for me than anything else."
His eagle was huge, considering Woods was right on his heels. Golf's biggest star fell three shots back following Singh's bomb, then dropped strokes with bogeys on the 16th and 18th holes to finish a 67.
"Just one of those things right now where I'm just a little hot at myself for how I finished," said Woods, who won this event three years ago at the Champions Club in Houston.
Woods had his best round of the week and still dropped a stroke, a testament to how well Singh has played and how difficult East Lake has been.
With rain consuming the Atlanta area over the past month and wind wreaking havoc this week, only 13 of the 30 players in the exclusive field are under par.
While Mickelson thinks he has a lot of work to do to win Sunday, Woods is not counting himself out. Asked how many strokes can be made up on a course as drenched as East Lake, Woods said:
"Quite a bit."
"It depends if we play lift, clean and place tomorrow or not," he said. "Every ball I hit, ball in the fairway, picked up mud, and it was clumps of mud. So I don't see how they are going to play it down."
"I would never have guessed that someone would have a three-shot lead on this golf course," Howell said, "simply because the premium that's put on making pars and birdies, how hard they are to come by."
Woods is looking to cap another sensational season with his sixth title but will have to hit more than five fairways in the final round, as he did Saturday. Despite his inaccuracy, he was cruising before the closing three holes.
"I need to step up there and just let it go, let it eat," he said. "When I do that, I'm fine."
Mickelson also hit just five fairways but made several clutch putts, including pars of 32 and 22 feet.
"I'm not really worried about what Vijay is doing," he said. "I have my own things to worry about."
Notable deaths of 2014 [PHOTOS]