Eleven years on, Woods has not won a major title since 2008 and Rose returns to Muirfield as the newly-crowned US Open champion and world number three following his brilliant victory at Merion.
Fittingly, it was a victory secured on Father's Day, with Rose recalling the influence of his late father Ken before that first round with Woods and Shigeki Maruyama in 2002.
"It was my first time ever playing with Woods and it was a big deal for me at the time," said Rose, who had won four times that year to become the top ranked Englishman at 41st in the world.
"He was arguably at the peak of his powers and clearly an intimidating force in the game. Guys were crumbling around him, he was winning tournaments by big margins. I had just had my first taste of success in the game, winning the British Masters in June and that's what got me into that pairing.
"I remember it being a big deal and I was worried about it. My dad gave me a pep talk that settled me down. He stayed up most of the night before thinking about what he could say to me to put it into perspective.
"He boiled it down to the fact that the family had dealt with much harder things with his illness. We were all facing the fact at that point that he was not going to be around much longer and that put into perspective what the round of golf really meant.
"That allowed me to just go out and play my game and not get caught up in the perception of what it was all about. I think I was four under after nine and shot 68. It was a day I was proud of and a nice memory for me with my dad."
That was not Rose's first taste of stardom at the Open of course. Four years earlier he had famously finished fourth at Birkdale as a 17-year-old amateur before turning professional the following day and missing 21 cuts in succession.
Since then his best finishes in the Open have been 12th in 2007 and 13th in 2009, but the 32-year-old can now attempt to join an exclusive club of which even Jack Nicklaus cannot claim membership.
Bobby Jones (twice), Gene Sarazen, Ben Hogan, Lee Trevino, Tom Watson and Woods are the only men to have won the US Open and Open Championship in the same year, something Rose would love to emulate at Muirfield.
"The Open Championship does stand out to me," he added. "I have a very special relationship with it which dates back to when I was 14 and led the regional qualifying event at my local club, and we know what happened in 1998.
"The Open is the one I have dreamed about winning the most for sure. As I play the next 10 years the Open is going to be at the forefront of my goals for a long, long time.
"If I'm allowed to dream, a career grand slam puts you into a whole different echelon. That makes you one of the greats of all time if that can be achieved. I feel my game suits all four majors. I don't think there is a weakness where that can't happen."
Rose finished 13th in the Travelers Championship immediately after his US Open win, but withdrew from the AT&T National the following week due to fatigue.
He feels refreshed after three weeks off and "itching" to return to competition, although he also enjoyed the chance to watch Andy Murray win Wimbledon from the Royal Box on Centre Court, where he had lunch with Wayne Rooney and Prime Minister David Cameron.
"Apparently David Cameron had tweeted me after my win but I didn't see it, so the first thing I did when he sat down was apologise for not replying," Rose added. "He said my win gave him his first line to Barack Obama at the G8 summit.
"It was fantastic to be there and I would not mind following in Murray's footsteps by winning the US Open first and then a major on home soil."