A five-shot lead was suddenly a manageable three shots and both McIlroy and new world number one Justin Rose are on -9.
Woods had a two-shot lead when his tee shot on the 16th nestled down in the rough.
Woods last shared the 36-hole lead at the Wyndham Championship in 2015. Rose showed his resolve after opening with consecutive bogeys, then rallying to shoot 68 to stay in touch with Woods.
McIlroy, who will be in the final twosome of the day with Woods on Sunday, said he only worries about himself. The last of his three PGA Tour victories was in 2011. He finished two back of Brooks Koepka.
Rahm was three behind at 136, along with Billy Horschel and Patrick Cantlay, each with a tournament-best 65, and Justin Thomas, the defending FedEx Cup champion who hit tee shots all over East Lake and somehow managed a 69.
With play still underway, the duo hold a one-shot lead over Gary Woodland (66) at four under.
If Woods wins in Atlanta, Golfweek has outlined all the other scenarios that must come to fruition for Woods to capture the third FedEx Cup of his career.
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He trailed by four at The Open Championship and PGA Championship, and was five back starting the final round of the Arnold Palmer Invitational presented by Mastercard, the Memorial Tournament presented by Nationwide and his most recent start, the BMW Championship.
"When I grabbed the lead at the Open Championship (it) didn't really feel abnormal, even though it's been years since I've been in those spots", he said. "I've got a bunch of guys behind me that have been playing well and are playing well, and we'll see what happens tomorrow". He birdied five straight holes from the third to the seventh, stretching his lead to as much as five. As much as he's done to get to this point, posting six top-10s this year in a comeback season that has defied belief, Woods has struggled to put four complete rounds together, and simply not been in this good of a position. "But I thought I could sneak it up there and get up on the upslope and have a good angle in there, and it just didn't work out".
"I got off to a nice start and made some nice putts", Woods said.
And so now the tournament heads to Sunday with a familiar focus, all eyes and hopes and narratives trained tightly on Woods and his crimson shirt.
McIlroy, for his part, says Woods is going to be tough to catch with such a big lead, but he just has to go out and play like he did today.
Only once since he joined the paid ranks in 2007, when injured a year ago, has McIlroy skipped Abu Dhabi.
"It's a little more unknown now", Rose said, when asked if it felt different to chase Woods on Sunday these days than in years past.