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If it was not quite a handing over of the torch, it was surely a glimpse of the future. At 39, Venus Williams has been spending more and more time looking in the rear-view mirror and in the 15-year-old American Cori Gauff she found an opponent who looked like her and played like her, only slightly better. And while Williams’s best days may be behind her, Gauff has many more to come.

Wimbledon: prodigy Cori 'Coco' Gauff makes fairytale debut Read more

In her first grand-slam match, having become the youngest player to qualify for the main draw, Gauff showed the talent and composure that is usually seen only a handful of times every generation as she upended Williams 6-4, 6-4 in the first round at Wimbledon, a grand arrival on the grandest of stages. She next plays Magdalena Rybarikova of Slovakia.

It was a shock because of the reputation of Williams, but really only because few people have had the chance to see Gauff play at the biggest events until now. In front of a packed No 1 Court, there was no signs of nerves, no fear of the five-times champion; she seemed calm as she put away one of the game’s best ever players with the minimum of fuss.

“I wouldn’t say I didn’t expect to win the match,” Gauff said. “I knew that I was going to go out there and play the way I play. I wasn’t surprised that I won. I mean, I was just overwhelmed at the end. I’ve never played on a court that big, the crowd was really wild. I was just surprised that people were cheering me on.”

Williams had won four of her seven grand slam tournaments, including two of her Wimbledons, before Gauff was born. Much as it was when Williams and her sister Serena arrived on Tour, there has been huge anticipation about the first sight of Gauff at this level. The youngest finalist in the US Open junior event at 13, she won the French Open juniors last year, shares a management group with Roger Federer and already has sponsorship deals worth more than $1m this year alone.

But despite the hype, Gauff seems grounded and her confidence does not quite spill over into arrogance, even when she discusses how good she thinks she may one day become. “I said this before: I want to be the greatest,” she said. “My dad told me that I could do this when I was eight. Obviously you never believe it. I’m still not 100% confident. But you have to just say things. You never know what happens.”

On the eve of her final-round qualifying match, Gauff stayed up late sitting a science exam. Nothing, not even playing on No 1 Court against a woman who inspired her to play the game, seems to faze her. “On my science test, I got a B,” Gauff said. “Today I’d give myself an A. Hopefully my next test I can get an A but you never know.”

Only when Williams dropped a final forehand into the net did Gauff, who prefers to be known as Coco, realise what she had done, falling to her haunches and putting her hands over her head. Her father, Corey, who had been jumping up and down in the stands throughout, was jubilant.

“On the court they were saying Cori [and] in the middle of the match I think random things,” she said. “I was just like, I hope my dad doesn’t think they’re cheering for him. He likes to say every time they call me Corey, they’re cheering for him. I was like, OK.”

Gauff broke in the fifth game and held the advantage to take the first set and having broken again for 3-2 in the second, her only moment of concern came when she dropped serve for 4-4. But Gauff broke again in the next game and clinched victory on her fourth match point. “I knew it was going to be mine, no matter what,” she said. “That’s why I just kind of hit my serves pretty hard.”

As for Williams, she has little doubt how far Gauff can go. “The sky’s the limit,” she said.