If this was the Woods of 15 years ago, he likely would be "the champion golfer of the year, " as they say over here, and have his name on the claret jug a fourth time.
"That's what I thought", said McIlroy. I don't know how she does it.
"I'm not getting ahead of myself, I'm just in a good position".
Despite pulling off one of his best performances in the past decade on Saturday, Woods ultimately came up short.
Woods underwent spinal fusion surgery in April past year and was arrested on suspicion of driving under the influence the following month when he was found asleep at the wheel of his auto.
He then took the outright lead while playing the 10th after another Schauffele bogey behind. "It didn't feel any different", said Woods.
Seven players had a share of the lead at some point.
That was certainly not true on the 18th, his tee shot seemingly destined to find the Barry Burn only to take a fortunate bounce to the right to stay on dry land.
Woods suffered no such woes, with gains at the fourth and sixth putting the most successful player in the field firmly in the frame. "It's all there, and it's moving in the right direction", he said.
Canada's Adam Hadwin shot 1-over (71) and sits tied for 51st heading into Sunday.
And the last two winners came from well back, Paul Lawrie starting the final round 10 shots behind in 1999 and Padraig Harrington being six off the lead in 2007, with both men eventually winning in a play-off.
If it wasn't exactly Tigermania, it was close.
Not since Woods in 2006 has the defending champion gone into the final round with at least a share of the lead.
With Rose and McIlroy in the clubhouse on six-under, Schauffele fought back from a 40-stroke outward nine to get to seven-under but Molinari was unflappable.
At the age of 42, finding a way to win is going to be a tall task.
"He chipped it beautifully", Woods said of Molinari. Moments later, Tiger Woods sent the gallery into a frenzy with three straight birdies to get into contention at a major for the first time in five years.
Woods had every reason to believe he would cap a most improbable comeback from four back surgeries. It's so special to have them aware because I've won a lot of golf tournaments in my career but they don't remember any of them. "I just need to regroup and get ready for tomorrow".
He quickly set aside his anger and produced a sublime approach shot onto the green - Molinari congratulating him as the passed - taking the applause of the crowd with a wave of his cap. He had to scramble to make birdie on the day's easiest hole, the short par-5 14th hole, but his 20-foot birdie putt kept his chances alive. I putted well. I holed out when I needed to.
Wood, who was fifth in the Open as an amateur in 2008 and third a year later, began the day eight shots off the lead shared by Zach Johnson and Kevin Kisner, but birdied the first, third, fifth, sixth and seventh to race to the turn in 31. But it was the middle part of his round that left him dissatisfied. "Today was a day that I had a great opportunity", Woods said.
Young gun Lucas Herbert is Australia's only other realistic hope after climbing to two under with a brilliant eagle the highlight of a second successive round of 69.
"Even though he's won 14, you have to learn how to get back", said McIlroy whose last major was in 2014.