Molinari, who lives in London with his wife and two children, had the temerity to birdie the 18th, that monster of a par four for a 69 and an eight-under total and that basically took the title out of the reach of American Xander Schauffelle, who ended up two shots behind in a tie for second with McIlroy, Rose and countryman Kevin Kisner.
While the rest blew leads, Molinari continued to bubble, recording an incredible 16 pars and two birdies on a day when the wind played havoc. And what made his success all the more remarkable was that he compiled it in the presence of Woods, just when he was contending once more on the final day of a major.
As Woods stormed into the lead around the turn and the galleries went into apoplexy, certain they were bearing witness to a special piece of golfing history, Molinari remained steadfast and carried on reeling off the pars.
On Twitter, his brother Edoardo - who he played with in the 2010 Ryder Cup - was imploring him to retain his composure. It was like asking the tide on the nearby North Sea to carry on going in and out. Molinari, the metronome, had been in pressurised situations with Woods before, most notably the final singles match of 2012.
Frankie, as he is known, kept his cool on that occasion to ensure the half point which completed the Miracle of Medinah and here he was again; puffing his cheeks now and again, but in the main, sending tee shot after tee shot down the fairway and then approach after approach into the green and, when missing, allowing his radically improved short game to do the business.
There were no bogeys on his scorecard and none of the other 79 players who made the cut could claim the same.
It was a deserved victory in every facet and although not a household name, it was far from unexpected on the range. He warranted his new standing as world No 6.
Molinari, always one of the best ball-strikers on Tour, has been red hot since May, when he fended off McIlroy down the stretch at the BMW PGA Championship. In his last two starts, he won the Quickens Loan National - which Woods himself promotes - and was second at the John Deere Classic a week ago.
Naturally the question will be "what will this do for Italian golf?" - yet just as importantly in the short-term is what this means for Europe. This ended America's stranglehold of the majors, ending their proud streak at five, and that will please Thomas Bjorn as much as the fact that Molinari has guaranteed himself a berth in September's Ryder Cup.
Anybody for another Woods-Molinari rematch?
Woods was as gracious as ever in defeat, and that must have been difficult after his 71 left him on five-under and in a tie for sixth. It is his best finish in a major in six years but it promised so much more. Woods double-bogeyed the 11th, bogeyed the 12th and notwithstanding the late roars of a mini rally with birdies on the 14th and 18th, he was a long way second best to his playing partner.
Molinari has an English swing coach in Denis Pugh, an English putting coach in Phil Kenyon and an English performance coach in Dave Alred, the former guru of Jonny Wilkinson. They should all bask in Woods' praise: "That was really, really impressive." Enough said.
