Molinari's playing partner Tiger Woods looked in line at one point to claim his first major in a decade. But while Woods faded after dropping three strokes in two holes at the 11th and 12th, Molinari kept his cool to shoot a second consecutive bogey-free round.
His 69 left him eight under par, two shots clear of his nearest challengers including Justin Rose and Rory McIlroy, three ahead of Woods and four shots ahead of last year's winner Jordan Spieth.
Molinari is a rare golfer from continental Europe to lift the Claret Jug — Sweden's Henrik Stenson triumphed at Royal Troon in 2016 but before him you have to go back to Seve Ballesteros in 1988.
The 35-year-old also finally delivered a major win for his country, going one step further than Costantino Rocca, who famously lost in a play-off to John Daly at St Andrews in 1995.
And he hopes his victory will have an impact back home in Italy, where Formula One is usually just about the only sport that competes with football for the headlines.
“The last round already was big news in Italy. Obviously, to achieve something like this is on another level,” said Molinari, who started the day six under par, three shots off the lead.
“Hopefully, there were a lot of young kids watching on TV today, like I was watching Constantino in '95 coming so close. Hopefully, they will get as
inspired as I was at the time, watching him vie for the Claret Jug.” Molinari, who lives in London and supports West Ham United, was not the favourite coming into the week but perhaps he should have been given his recent form.
He won the PGA Championship at Wentworth in May and recently claimed his first victory on the PGA Tour at the Quicken Loans National. He was also the runner-up at last year's US PGA Championship.
Contributing to Molinari's success has been a performance coach called Dave Alred, who used to work as a kicking coach for England rugby star Jonny Wilkinson. The improvement in his game is a huge boost for Europe as they aim to reclaim the Ryder Cup from the United States at Le Golf National near Paris in late September.
Molinari has been there before — he and his brother played in the European team that won at Celtic Manor in 2010, while Francesco's half with Woods gave Europe victory at Medinah in 2012.
“There's going to be a lot of European guys vying for his partnership in the foursomes at the Ryder Cup, that's for sure,” said McIlroy.
Meanwhile, the Americans will be particularly wary of the Italian after his outstanding performance in Carnoustie. “He's been playing unbelievable golf. He's been working his butt off. I see him in the gym all the time, going through his routine, grinding on the range, doing his own stuff,” said Spieth.
“It truly is hard work that paid off for Francesco. I'm certainly happy for him.”
By Andy Scott