Like the rest of the game's élite, he had to acknowledge that even with the Tiger's putter almost as cold as charity he could still open up a gap perhaps unprecedented in any sporting age.
The gap, that is, between Woods and all those who labour to match the scale of his talent and the depth of his creative imagination; the chasm between men of talent and professionalism and those touched by both genius and some ultimate nerve.
You have to delve into the past to find such an example of one man cutting away the rest of his sport quite so surgically. Muhammad Ali did it sublimely in the boxing ring and now Woods does it almost at will. Some thought the momentum of his drive for a record number of major triumphs was wilting; the spring of his extraordinary brilliance was running dry.
But as the sunlight dwindled on the coast of Fife such such suppositions were exposed as the illusions and the wild hopes of the under-manned and the outgunned.
In 1997 Montgomerie, on the third day of the US Masters, watched in dismay as Woods unleashed a form of golf with which even Jack Nicklaus was unfamiliar.
That day the 21-year-old took a massive, game-changing stride towards his first, record-engulfing Masters, and the Scotsman was the unfortunate victim of the brilliance in a match that would have been stopped under the rules of the Marquess of Queensberry.
Yesterday, here on the mother of courses, the 29-year-old won his second Open and 10th major title. History, cruelly, fell upon the 42-year-old Scotsman whose career had been so dramatically resurrected over the previous 48 hours.
Montgomerie did not disgrace himself. Indeed, at one point he was within a shot of the man who last Friday officially picked up the baton of greatness from the retiring Nicklaus.
But it was then that Woods became quite savagely assertive. He didn't so much put Monty to the sword as the out-tray. The Scotsman had applied for a late run at glory, a register on the roll call of significant champions, but Woods scrawled a response that did not permit a challenge. It said, simply: Rejected.
Montgomerie, bedevilled by a devastating divorce, a fever of resentment by some fellow pros who believe that he seriously bent the rules in the Indonesian Open, and a hurtful refusal of the Augusta National to grant him an invitation to the Georgian major in the spring - which was won rather more hazardously by Woods than in his triumph here - should take none of this personally.
Every professional who fell behind Woods here at the 134th Open - the American led all the way but for a few brief moments last Thursday - is obliged to pick up his life this morning with a distinct sense he has been reduced to the category of second-class citizen.
This was the astonishing reality in the humid evening when Woods came home a winner by five strokes over Montgomerie. That, as it happened, was three fewer than when he claimed the Open title for the first time here five years ago. But no-one should see in this oddity a hint of decline, of ebbing powers.
Woods has reconfirmed his commitment to the idea of marching down on Nicklaus's all-time mark of 18 major victories, and when he ran to embrace his mother Kutilda - who had watched her son's final winning stroke from the old clubhouse balcony - there was an overwhelming sense of a re-seeding of ambition, a new resolve to push back the boundaries of individual achievement.
In all of the past few days there has been an element of the inevitable, a belief that here at the course which has always been considered the classic guide to the range of any golf game, Woods was intent on more than merely picking up another bauble on the way to the Nicklaus mountain-top.
It was here that Nicklaus had twice won the Open, in 1970 and 1978, to establish himself as a legend of the game on both sides of the Atlantic, and where the Golden Bear had decided to say his last farewell to competitive golf.
So what was Woods' response? It was course management that brought more than a flash of envy from Nicklaus, who said on his first sighting of the slim youth from California that he would win more Masters titles than himself and Arnold Palmer put together.
This week the transfer of power was only symbolically passed on. In reality it happened in 2000 when Woods performed the extraordinary feat of a calendar Grand Slam. Yesterday he joined Nicklaus on the lonely pinnacle of multiple victories in all the major championships, and it was impossible not to believe he had returned himself to the tide of golfing history.
When he was asked what this latest triumph said to those who doubted his capacity to maintain his domination over the game, he smiled with a perhaps misleading affability and said that he couldn't say it on air. If he had taken that liberty, he might have said that winning any golf tournament is a test of skill and nerve and to win majors with such consistency, and authority, was something that just didn't happen. You had to suffer a little pain. You had to re-make your swing. You had to look to mirror and ask if it still mattered enough.
The Tiger provided a crushing answer to that last question as all of his most serious rivals, one by one, gave up the unequal battle.
Montgomery's challenge lasted longer than those men who had beaten him to the prize that haunts him, a major title ... men like Jose Maria Olazabal, a double Masters winner, Retief Goosen, the quiet South African with two US Opens to his name, and the currently disaffected Ernie Els.
Montgomerie refused to buckle on Saturday and yesterday, on the ninth hole, he drew within a shot of the man whose rise seemed to most rebuke his own failure to land the major titles that he always believed he needed to define his extraordinary talent. There was a spring in Monty's stride then, a dawning belief that he might just make the most important breakthrough of his professional life.
But then the Tiger, who in his victory speech made it clear he had not been too impressed by the more partisan supporters in the vast galleries when his battle with Monty became most fierce in the third round, decided it was time to get down to the most serious business.
Woods produced the kind of authority that if he were a heavyweight boxer might have persuaded an opponent to stay on his stool. To Colin Montgomerie's credit, he did not do that.
He simply subsided, along with all of the Tiger's peers. He acknowledged, sadly but without a sliver of doubt, that the battle was hopeless.