It was at Candlestick Park, the old wind-blown stadium sticking out into San Francisco Bay, 14 years ago when Montana, bidding for a place in his fifth Super Bowl, was blind-sided by Leonard Marshall of the New York Giants. Later, in the locker-room Montana's skin had the deathly quality of old parchment, and you knew he would never be the same again.
The memory flickered here on Sunday night because Brady, another huge stride along the way to being the new Montana, the new Mr Cool, after his third Super Bowl triumph, was speaking so passionately about about the platform for success he enjoys under the brilliant coaching of the now officially dynastic Bill Belichick of the New England Patriots.
You thought of the crushing reality which came to Montana because Brady's life has acquired the full-blown status of an American dream, and such a thing cannot last, surely, in the unremitting pressure of a game in which so many star players cannot face the day without a shot of painkiller.
Brady, though, at 27 years - the youngest age at which a quarterback has ever done so much - seems so immune from risk or crisis in his sporting Camelot.
There were, for example, certain points in Super Bowl XXXIX when the Philadelphia Eagles, a talented, wounded team aching from three successive years of failing one step away from a Super Bowl, seemed they might just be about to smash down the world of Brady and his now hugely celebrated mentor, Belichick.
But each time the coach, who after Sunday's victory has a superior post- season record (10-1) to the legendary Vince Lombardi, had a ruse and Brady had the nerve and the technique to make it work.
Once again, the Patriots triumphed, as they did in 2002 and 2004 against the St Louis Rams and the Carolina Panthers, by a mere three points, yet when the Eagles were beaten, 24-21, an eerie conclusion reached into every corner of the Alltel Stadium.
It was that deep down young Brady had never been imperilled. Later he said: "Why would anyone want to leave a team which has a spirit like this? For months on end, your life is just football, you're up at 6am in the morning, you're working on new schemes, new challenges, and why? Because you want to get to the Super Bowl, you want to be the best. The players here know that they will never get a better chance of winning. You know it cannot last for ever, but you want to hang on to it as long as you can. Coach Belichick understands all the needs of his players. He gives us certainties about what we are doing."
Some cynics believe that before suffering the ambush that befell Montana, Brady will experience another kind of moment of truth - one in which he will ask himself if, after accumulating the Super Bowl rings and all the glory, whether at some point he should also enjoy all the financial rewards due to arguably America's most revered young sportsman. The fact is that under the Patriots' strict salary capping, Brady cannot expect to compete with the rewards already handed out to his Indianapolis Colts rival, Peyton Manning, and still less those of the White Sox slugger Magglio Ordonez, who is reported to have been lured to the Detroit Tigers on a five-year contract paying $75m (pounds 40m).
At what point does the Brady dream impinge on real life? Belichick's key assistants, Charlie Weiss, the offensive co-ordinator, and Romeo Crennel, who is in charge of a superbly pragmatic defence, have paid quite as much homage as Brady to the mystique of the leader Belichick and at the end of Sunday's game the three coaches went into their own emotional huddle. This was partly due, no doubt, to the fact that Weiss this week take up his duties as the coach of Notre Dame University, one of the most fabled assignments in all of American football, and Crennel is considered a certainty to take over the Cleveland Browns.
In an age of free agency and a floating player population, how long can Belichick hold together his empire? "You get through one season. You do your job as best you can, and then you face the future," says Belichick. "Personal ambition is a vital part of the game. I'm just happy that we have something here that seems to attract so many fine players."
Certainly, Brady did not have the monopoly on glory in the Alltel Stadium. The most valuable player award, which he snaffled up in the earlier Super Bowl triumphs, this time went to his inspired wide receiver Deion Branch, who made 11 receptions, some of them stunning in their nerve and precision under fire, which equalled the record of the great Jerry Rice of San Francisco. The linebackers Mike Vrabel, who also scored a touchdown when he switched to the offensive squad, Willie McGinest and Tedy Bruschi all played with unrelenting application and sharpness and the safety Rodney Harrison was a human wrecking ball.
However, the Eagles all-pro safety Michael Lewis had no doubt about the man who had hurt his team most. "Brady killed us just when we thought we might be getting on top. He releases the ball so quickly, he reads off the play in a way that is uncanny. I've no doubt in my mind - he's the best quarterback there is."
It was a verdict from the trenches which can only enhance the burgeoning legend of Tom Brady, the clean-cut successor to Mr Cool. Yet it does not quite dissolve that picture of the huge New York Giant coming out of the blindside
and making Joe Montana feel old. There are no doubt more perilous places than the gridiron to live a dream indefinitely. But perhaps not many.