Tiger, once regarded as the greatest golfer in the world, has won 14 major championships in his legendary career - having won every major at least three times between 1997 and 2008.
Then it fell on Rose who almost had an albatross at 14 and finished at six-under, and then on Rory McIlroy as he roared back into view with a 30-foot putt for an eagle three on the 14th, a bomb that exploded in cheers all over the course and gave the Northern Irishman a share of the lead.
"I've always wanted to battle it out in a major with Tiger".
Other top players weren't as fortunate. Rose's only major to date is the 2013 US Open, although he came agonisingly close at the Masters a year ago before losing to Sergio Garcia in a play-off.
Tiger Woods powered into the reckoning at Carnoustie and Jordan Spieth made a stunning start to take a joint-share of the lead as moving day lived up to its name during Saturday's third round at The Open.
"Clearly, in my group, the attention wasn't really on me, let's put it that way", said Molinari, 35, sitting in the media interview room with the glistening Claret Jug at his side.
"It will be a pretty packed leaderboard, and I'm certainly right there in it", Woods said. I don't know how she does it. I received a lot of good wishes.
The 14-times major victor had to settle for a closing 71 and a 279 aggregate.
A birdie at the 14th allowed him to hang around, but ultimately his even-par 71 to get in at 5 under was three shots short, as Francesco Molinari won at 8-under 276. "I need to go get it", Woods said. So I think that was one of the key moments. However, it proved to be a false dawn as three dropped shots in two holes saw him fall behind and in the end the 14-time major victor was being consoled by his two children. "I've got a chance at this, which is great".
He was pumping his fist and even raised a two-fingered V for victory to the gallery at the fourth as he sank a longish birdie putt to move to three off the lead. Woods was also close to birdies on the 13th and 15th but did escape damage on the 18th by making par after hitting the wall of the Barry Burn.
Twelve players were separated by four shots, a group that includes Rory McIlroy, Tommy Fleetwood and Zach Johnson.
A miss-hit flop shot at the 11th ended cost him a double-bogey that stopped him in his tracks and although he birdied the 14th to stay in the hunt he fell just short, finishing in a tie for sixth on five-under.
"I felt good about the range session".
"Unfortunately in golf there's only one victor, this time it's me! The golf course was gettable".
He reached the turn in 34 strokes and with Spieth and Schauffele imploding a few holes back Woods was suddenly clear at the top of the leaderboard on seven-under.
Molinari teamed up with his brother Edoardo in the Ryder Cup in 2010 and scored a half point against Woods to secure outright victory in his singles match in the 2012 competition in Chicago, dubbed the "Miracle of Medinah" after Europe fought back to win from a seemingly impossible position.
"Sometimes I have a few drinks, " said Pepperell, who finished as Woods was in the lead.
Woods, however, will not yet allow himself to consider how he might feel should he succeed. Obviously, the benefit of playing this morning is I get to recover a bit quicker than they do. "Next thing, lo and behold, I'm tied for the lead, and then I'm leading it".
Ideal conditions in the third round led to a number of low scores, including a 64 by Justin Rose and 65s by Spieth and Francesco Molinari.
"It will be more hard tomorrow in the wind for sure", Spieth, who launched his third round with an eagle after driving the first green and then took full advantage of the ideal scoring conditions, told reporters. "Tiger is minus-7, he didn't have a drink last night, I bet".