On a dramatic final day on which the lead changed hands many times, a birdie at the final hole gave Molinari an 8-under-par total of 276, making him the first Italian ever to win a major. He had to scramble to make birdie on the day's easiest hole, the short par-5 14th hole, but his 20-foot birdie putt kept his chances alive.
The charge had the golf world on fire, and many dreaming of that 15th major finally arriving 10 years after his 2008 U.S. Open triumph.
Tiger Woods' fairytale of a 15th major and first for 10 years looked a very distinct possibility when he took the lead with nine holes to go, but the former world No.1 struggled over the back nine to fall away.
Woods also paid a glowing tribute to his playing-partner Molinari, who was the only player to keep a bogey off his card in the testing conditions of the final day as he fired an impressive 69 to win by two shots. Rose's only major to date is the 2013 US Open, although he came agonisingly close at the Masters previous year before losing to Sergio Garcia in a play-off. Late on Friday, Anirban Lahiri missed the cut after a second round 74 following his first round 76 to finish at 8-over as the cut fell at 3-over.
Ominously for the others who will start with high hopes on Sunday, Spieth appears to have played his way into top form with impeccable timing.
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He was three shots behind the leaders, who had yet to tee off in the afternoon at Carnoustie. "Then ask me again".
"It seemed like everybody was shooting six, seven under and I figured I could probably do the same and I needed to with the leaders starting at six".
He then made a two-putt birdie at the lengthy par-five sixth hole to get two two-under. Hopefully, there were a lot of young kids watching on TV today, like I was watching Costantino in '95 coming so close.
However, two holes later he dropped a shot after three-putting at the short 16th, and a rueful shake of the head confirmed his disapproval.
It is four years since the 29-year-old last won a major - at the 2014 British Open at Hoylake - but he believes his extra know-how could count in his favour when the winds are expected to gust up to 28mph on Sunday. Schauffele made a double on the next hole after getting tangled in the rough, and all of a sudden Woods was alone atop the leaderboard.
England's Justin Rose is a shot behind Woods and McIlroy after earlier equalling the lowest score in an Open at Carnoustie with a brilliant 64, a day after needing a birdie on the last just to make the cut.
The 42-year-old's much anticipated return to The Open after a two-year hiatus had been a bit of a damp squib on the first two days at Carnoustie. Fleetwood, who dropped three shots in two holes on the back nine on his way to a 71, is part of that group. "I'm really feeling more comfortable with the long game". And doing so a year after his fourth back surgery.
I mean, there was everything to make someone nervous, but I focused on my process and on hitting good shots and on playing smart golf.