There is nothing like putting your experience to good use.

So when Matthew Fitzgerald sent his 7-iron approach shot flying into deep rough to the left of the 17th fairway, I knew my moment had come. It was time – and you might like to hum the Thunderbirds theme tune at this point – to go to his rescue.

Now I'm not going to lay claim to any supernatural powers here, but the combination of a vicious slice and a miser's indignation about the price of modern golf balls has led to me spending many hours of my life thrashing about in waist-deep Scottish weeds in pursuit of errant (and, by the way, disgracefully expensive) Titleists. And as there was something of the little-boy-lost look on Fitzgerald's face at that point, he needed me on his side.

Actually, Fitzgerald seemed to have rather a lot of us on his side. Russell Henley, his American playing partner had actually sprinted into the rough to mark the approximate spot where the ball had gone, while a posse of spotters, scorers and others were soon peering and prodding for all they were worth. But years of training were always going to pay off, and I duly found Fitzgerald's ball.

"Eh, thanks," he muttered. Well, there's a limit to the gratitude that can be summoned as you gaze down at an impossible lie. Fitzgerald, who was being chaperoned round Muirfield by Lorne Duncan, the wisest old owl in the caddy shack, accepted the inevitable and took his penalty drop on a well-trodden patch of grass nearby.

Fitzgerald still ran up a double-bogey, but it could have been worse. And the significance of the episode was that the 18-year-old squeezed into the Open's third round one shot inside the cut line, at seven-over-par. Enjoy your weekend, lad. You – well, we actually – deserve it.

Okay, so he rode his luck. But almost everything else the Sheffield teenager has done at this Open Championship has confirmed the rumour that a great new talent has been born. The first reigning British Boys' champion to win a place in the Open field since Sergio Garcia in 1998, Fitzpatrick has the game and the level-headed outlook to suggest that he will be playing in major championships for years to come.

Fitzgerald's group may have been one of the most callow ever assembled at the Open. As well as himself and the 24-year-old Henley, it also included Jordan Spieth, the 19-year-old American who had become the first teenager in 82 years to win a US Tour event when he took the John Deere Classic title – and the last remaining slot in the Open – in Illinois last weekend.

Their combined total of 61 years is two less than Tom Watson has spent on this earth. Watson had played a round with Fitzgerald on Tuesday, and praised the young Englishman's mature approach to the game. Not that his Fitzgerald's maturity was apparent to the practice range official who thought he was fetching balls for Tiger Woods, or the disbelieving locker room attendant who demanded to see his credentials before letting him in.

In fairness, Fitzgerald looks even younger than 18. he's the kind of fresh-faced fellow who will probably be obliged to carry ID until he's 30, but the sheer improbability of his feat in even getting into the Open could be measured by the fact that Jodie Chubb, his group's scoreboard carrier, is the same age as him.

Of course, golf has seen a few young bolters down the years. The most obvious point of reference for Fitzgerald is provided by Justin Rose, who was just 17 when he lit up the 1998 Open at Birkdale. It is also worth remembering that Rose went through a couple of years of pain afterwards, missing a succession of cuts before he established himself as a European Tour player.

There was also the case of Tom Lewis, who launched himself into a professional career straight after his impressive performance at the Royal St George's Open two years ago. Lewis actually won a tournament early on, but he has struggled at times since.

Fitzgerald, though, has other plans. In a couple of months time he will be heading to Chicago to take up a golf scholarship at Northwestern University, the alma mater of Luke Donald. And whatever happens over the next couple of days, he will go with a lot of good memories, and a lot wiser for his time at Muirfield.

"I've learned a lot," he beamed. "I've played with a lot of nice guys. Every player has been fantastic, and hopefully it won't be too long before I'm playing regularly with them.

"I've felt that I can play with these guys. In the practice rounds the guys were maybe not taking it that seriously, but I certainly hit it as well as most of them. I was two-under on the front nine on Thursday, which was right up there. That is evidence that I can play and gives me confidence that I can compete."

Well, up to a point matey. Sometimes you need a little help as well – from an expert in his badly overgrown field.