James Lawton: Rory and Tiger may be able to create golf's latest great rivalry

You have to believe in your ability to win – not so easy against Tiger on the last day

Of all the challenges facing Rory McIlroy here the greatest may well be the need to fight his way out of a time warp.

It is one Tiger Woods may just have created with his comeback victory in Florida eight days ago.

There was such authority, such old but still familiar swagger in his stride at Arnold Palmer's Bay Hill, that it was as though he had reached out to turn back the clock.

How far? The tempting theory is that it was 10 years, back to Augusta 2002 and the last time it seemed that a new generation of golfers had found the nerve to curb, if not humanise, the man who many believed had changed the nature of the game.

At 22, McIlroy may well have banished the swarm of demons which engulfed him here this time last year. If anything could free him from the oppressive memory of such trauma, it was surely his sublime taking of the US Open a few months later.

But then McIlroy, for all his precocious brilliance, has one major; neither Lee Westwood nor Luke Donald has one; and the Tiger has 14 – and maybe a rekindled belief that he can do again what he did 10 years ago. Quite simply, he bullied the most dangerous of his rivals into the belief that in the end they couldn't win.

They could play some of their best golf – and we are talking here about major winners like Ernie Els, Vijay Singh, Retief Goosen and a Sergio Garcia still filled with the youthful belief that any day he would join their company – and they could go into the final day buoyed by the thought that they had laid down the foundations for glory along the back nine on Sunday afternoon.

Yet one by one they fell apart and, naturally, the Tiger grew stronger every time he heard a groan or a sigh from some neighbouring gallery.

Later, the anguished Els, the owner of a swing so pure that he had no need to stand in any man's shadow, admitted that when he imploded on the way out of Amen Corner it was, more than anything, because he knew that whatever he did he couldn't get the Tiger out of his mind.

"You have to believe in your ability to win in any situation," he said, "and that is not so easy when you are up against Tiger on the last day. You know he is not about to let go and this knowledge magnifies every mistake you make.

"I believe that no one is going to break his hold on the game until that mindset is broken. We analyse his game, look for weaknesses, but all the time we cannot forget his mental strength. It is very hard to match."

It was soul-baring candour at the end of a day on which Els – who is missing this week for the first time since those days when he was one of the principal glories of the game outside of the shadow of the Tiger – Goosen, Singh, the winner two years earlier and a man of the most formidable powers of concentration, had all submitted to the intimidation.

Goosen, who already had the notch of a US Open, went into the last round two shots ahead of his playing partner Woods. But he shrivelled in the early action. He finished three shots adrift. He started as one of those who believed that it was time to take on the Tiger on their own terms.

If anyone is entitled to believe that he is capable of such a feat, after the years of the Tiger's decline, it is surely McIlroy, who while winning the US Open, and becoming arguably golf's ultimate Redemption Man, displayed a touch and a vision which shattered no fewer than 12 records. This was work from a young man golf hadn't seen since the Tiger's first great eruption at Augusta in 1997.

McIlroy was one of the first to say that the aura of the Tiger had diminished, that if he had always to be respected for his achievements, he was no longer a figure of awe – and certainly not the man who had provoked such contagious panic in 2002.

He was saying the other day: "I'm in the place where I always wanted to be. I love playing in the spotlight. I'm a lot more experienced as a player and a person as I was a year ago. I definitely feel I'm a much more complete player."

It is a dazzling possibility when you consider the scale of his game at the Congressional Country Club last summer – and his impact at St Andrews in 2010, when his 63 was the lowest first-round score in 150 years of Open history.

Yet if these were the spectacular statements of the most arresting talent to emerge since that of the man he hopes to break down here on Sunday afternoon, the mere idea of it happening is not yet calculated to burn off the field. That, a decade on, is still the unique strength of Tiger Woods.

Will Tiger v Rory live up to game's greatest duels?

JH Taylor v James Braid v Harry Vardon

Known as "The Great Triumvirate", the three Britons combined to win the Open Championship 16 times in a spell of 21 years from 1894 to 1914. And in the five Opens they didn't win, one or more of them were runners-up. The trio revolutionised golf, with Vardon the leading member. The former gardener became the first international golfing celebrity, heading to the United States to play in a series of exhibition matches. He remains the only six-time Open champion.

Gene Sarazen v Walter Hagen

When Sarazen won the 1922 US Open at the age of 20, Hagen was 30 and already had four majors to his name. The rivalry was obvious and was given extra spice by the tension between the pair. Straight from the off, the two Americans did not get along. After Sarazen had won the USPGA following the US Open, the duo met up for a challenge match. It was so much more than an exhibition. "I didn't like the way he kept calling me 'kid'," said Sarazen. "I was a champion and I wanted Hagen to respect me as a champion." He won three-and-two, although in the long term he lost, recording seven majors to Hagen's 11.

Sam Snead v Ben Hogan

"Slammin' Sam" may have outscored Hogan in tournament wins, 82 to 61, but in the pantheon he still comes second best to the man considered the most professional of all professionals. They were born the same year (1912) and would compete against each other for almost four decades. Snead actually had a 4-0 play-off record over Hogan (including the 1954 Masters), yet probably because Hogan won four US Opens and Snead drew a blank, the latter left the bigger legacy. "The three things I fear most in golf," said Snead, who won seven majors to Hogan's nine, "are lightning, Ben Hogan and a downhill putt."

Arnold Palmer v Jack Nicklaus

The greatest of all golfing rivalries. Palmer came from a poor background, Nicklaus was privileged; Palmer was made for Hollywood, Nicklaus was a chubby kid with a crew-cut; Palmer drew the ball, Nicklaus played with a fade. Inevitably, Nicklaus, 11 years the younger, became the enemy of "Arnie's Army", which seemed only to spur him on. In the 1962 US Open, his first major as a pro, Nicklaus dared to take the crowd favourite to an 18-hole play-off – and proceeded to beat him. Although Palmer was to win two majors that year, Nicklaus proved his superior with 18 majors.

Tom Watson v Jack Nicklaus

While he was once the kid giving the old master a lesson, Nicklaus was to see his role reversed. Watson was the kid from Kansas who was to ensure that Nicklaus's second phase as the game's greatest champion would not be straightforward. Their rivalry was always good-natured and was gloriously summed up in "The Duel in the Sun". At Turnberry in 1977, Watson beat Nicklaus by a shot after an epic battle. Indeed, four of Watson's eight majors came at the expense of Nicklaus.

"I'm tired of giving my best and not having it be good enough," said Nicklaus. Of course, it often was good enough and Watson was in the chasing pack when Nicklaus won the Masters in 1986 as a 46-year-old.