Woods, a two-time victor of the tournament, carded six birdies in his opening seven holes during his third round, opening up a five-shot lead at one stage.
This is the first time Woods will be competing in the Tour Championship for years after returning to top form this season.
It will be the first time Woods and McIlroy (66) play in the final group Sunday on the PGA Tour. Rose, who made a bogey at the opening hole as Woods converted from 30ft for a birdie, was amongst those battered by a Tiger tsunami. You've got to keep hanging in there and make a lot of pars and I did that today ...
Woods has only lost twice in his career when leading after 54 holes, but in each of those losses his lead was two shots or fewer. We've seen glimpses of vintage Woods, but he hasn't put together a comprehensive performance until now.
Tiger Woods turned back the clock about 15 years Saturday - at least on the front nine of Round 3 at the Tour Championship. He has flirted with victory this year, surging late to finish second at last month's PGA Championship and posting three other top-sixes since the start of July, but never before has he been so within reach of ending his hard, complicated drought. "Good Lord", Woods said afterwards. "I was hitting it absolutely dead flush, the putts I was hitting were going in and from there I just tried to hang in there". "I've got a bunch of guys behind me that have been playing well and are playing well".
Starting in a share of the lead with Rose, the 14-times major champion rattled home birdie putts in six of his first seven holes.
In past years, McIlroy normally appeared at the BMW PGA Championship at Wentworth in May, although he did skip the European Tour's flagship event in both 2016 and 2017. Two bogeys coming in, however, including a great save on the 16th when his first chip shot rolled back down a hill guarding the green, cut into the lead.
There used to be no chance against Woods when he was atop the leaderboard going into the final round. This is a spot I'd much rather be in than four or five back. "I'm certainly much more equipped than I was in March because of what I've gone through". I always feel I start the year a little bit behind everyone else because I have to go over to Europe. 'It's the flawless place for me to open my campaign, ' he said in January, 'but the landscape has shifted dramatically.
"I don't have to shoot 63 or 64 and hope I get help".
"The crowds were electric because of it, " Rose said.
Woods has had four finishes in the top 5, a runner-up by one shot at Innisbrook and by two shots at the PGA Championship.