Waking up on a Monday morning can be a fairly agonised palaver as you wearily paw at the alarm clock before making a despondent shuffle towards the kettle amid a gaping torrent of groaning yawns.

The Monday blues eh? Not if you’re Francesco Molinari. “Waking up with the Claret Jug on my bedside table was amazing,” said the new Open champion with a sense of buoyant if bleary-eyed reverence.

“But I didn’t want to go to bed. It was nice toasting the win with champagne and clinking the glass against the spot where my name is engraved.

“I wanted to stay awake as long as possible looking at the trophy to make sure it really happened. It’s not a nice feeling when you let it out of your sight.

“And you are afraid you will wake up and it was all a dream. Thankfully, it was still there when I woke up. I grew up in Italy dreaming of winning this tournament. And the reality is even better than the dream”

In the company of Tiger Woods, on a spell-binding Sunday at Carnoustie that had more twists than a bowl of fusilli, the calm, collected 35-year-old secured Italian golf’s greatest conquest.

Amid the intolerable tension, it was a case of Forza Molinari. And as for Woods? Well, he still provided another chapter in the Tiger tale when it comes to Italy’s own golfing story.

“It’s funny how he seems to be involved in some of the greatest moments for Italian golf,” noted Molinari.

“Costantino Rocca’s win over him in the Ryder Cup (in 1997) was huge news in Italy. Then I had a half with him in the singles at Medinah in 2012, then I won his tournament for my first win in America (the Quicken Loans National) and now I played alongside him and won the Claret Jug.

“I can admit it makes it even more special that I was playing alongside Tiger when I won the Open, and that he was like the old Tiger, fighting hard for the trophy and playing unbelievable golf.

“It was funny that I heard players like Jordan Spieth saying it would be great to have Tiger involved in a real shoot-out at the majors again. I can say the same thing now … but not before. Be careful what you wish for.”

Golf may be buried under the mountains of coverage dedicated to football and motor sports in his native land but Molinari’s victory was front page news. With his brother, Edoardo, these siblings from Turin have been doing their best to make the headlines. They don’t come much bigger than an Open championship win.

“There is not the same tradition of golf that you find in other countries so myself and Edoardo always felt we had to prove ourselves a little bit more, that we really belonged,” he added. “Maybe that fighting spirit helped me to achieve this victory?”

The inspiring feats of the aforementioned Rocca, who famously holed an astonishing putt up through the Valley of Sin in the 1995 Open and almost pounded the green flat in jubilation, continue to resonate.

Rocca, of course, lost that Open in the subsequent play-off which followed that putt but Sunday’s success was something of a redemption. “He is my hero, my idol, my mentor and this win is for him as well as for me,” said Molinari.

Back in Italy, meanwhile, the elder Molinari brother was savouring his sibling’s success.

“When we were younger, we would always have a few putts when we practising and say, ‘this is for the Open, or the Masters, or the Ryder Cup’,” reflected Edoardo. “Every young golfer probably does that at some point. And now, Francesco has lived that moment out. A six-foot putt to win the Open? It’s great.”

There may be more to come. “If he keeps playing like he has the last two months, he’s going to win a lot of majors,” he said. “In golf, the hardest thing is to keep playing consistently well over a period of time. Hopefully he can do that.”

Edoardo, 37, hadn’t spoken to his brother in the whirlwind hours after his Open win – “he’s been a bit busy” – but the conversation, when it happens, “will be quite emotional.”

From the amateur game to team-mates in the Ryder Cup, the Molinari duo came through together and for a spell it was Edoardo who was blazing the trail.

His historic win in the 2005 US Amateur Championship earned him a place in the following year’s Masters. Francesco went along as his caddie and they played alongside that man Tiger.

“Tiger was always portrayed as someone very selfish and quiet on the golf course but in that year we both got the opposite impression,” said Edoardo.

“We had a great time in the Masters with Tiger. Francesco and I had grown up together, we spent all our time together on the course. To be able to have him with me at the Masters was very special. In the years that followed, we played all the majors together as professionals. This win is is the icing on the cake.

“Our relationship was based on a very good healthy rivalry. I was the older brother and was the example and maybe someone he needed to beat to keep improving.

“He has become the best of the two of us over the last few years. When we were young, he was a bit more intense. But as soon as he started playing seriously he channelled that the right way.

“He was always very hard but he kept calm on the course and that’s the best attitude you can have as a golfer.”

In 2010, aided by a brace of wins in the home of golf in the Scottish Open at Loch Lomond and the Johnnie Walker Championship at Gleneagles, Edoardo reached a career high of 14th on the world rankings.

Injuries and a loss of both form and his tour card have led to a period of struggle but a win in Morocco last season, his first on the main circuit in seven years, completed his clamber back from the depths of despair.

“When you are playing poorly, you can always do something,” he said of that frustrating, downbeat period. “But when you are sitting on a couch with your hand in a cast there’s nothing you can do. Those were the low moments and Francesco helped me through those times.”

These are now the high moments that the Molinari brothers are savouring. Francesco’s Open triumph has lifted him to No 6 on the world rankings.

Edoardo, meanwhile, has just one top-10 on the tour this season and is down at No 397 on the global pecking order.

In this game, though, fortunes can swiftly change. And you can’t let your younger brother steal all the praise and plaudits.

“I still have big ambitions,” said Edoardo. “If I didn’t have those I would be doing something else. I’m still working hard and still hoping to catch Francesco one day.

“As crazy as that sounds straight after he’s won an Open, I’m still hopeful that one day I can play the kind of golf he is playing right now.

“I’ve proved that before. You have to take his success and use it as an inspiration.”

As Francesco savours his Open glory, it’s a case of big brother is watching you as Edoardo plots a route back to the top.