Fifteen-year-old Cori Gauff produced one of the great Wimbledon debuts by beating Venus Williams – and then set her sights on the trophy.

The American is the youngest woman to qualify for the tournament in the Open era but she played like a veteran in a superb 6-4 6-4 victory against a player 24 years her senior who had won four of her seven grand slam singles titles before Gauff was born.

Gauff was inspired to pick up a racket because of the Williams sisters, and she thanked Venus at the net, saying: "I wouldn't be here if it wasn't for her – I told her she was so inspiring and I've always wanted to tell her that but I've never had the guts to before."

But it quickly became clear Gauff, who sat an online science exam at 11pm before her final qualifying match, was not going to be overawed by the occasion and she made just eight unforced errors during the match.

Asked how far she thinks she can go, she said: "My goal is to win it.

"I want to be the greatest. My dad told me that I could do this when I was eight. Obviously you never believe it. I'm still not 100 per cent confident. But you have to just say things. You never know what happens.

"If I went into this match saying, 'Let's see how many games I can get against her', then I most definitely would not have won. My goal was to play my best. My dream was to win. That's what happened.

"I think people limit themselves too much. Once you actually get your goal, then it's like, what do you do now? I like to shoot really high. I always have many goals along the road, but that way you have the ultimate goal."

Williams was understandably disappointed after only her second first-round loss since her debut in 1997, but she was hugely impressed by Gauff and said of her conqueror's potential: "I think the sky's the limit, it really is."

While Williams has been setting records at one end of the age scale, Gauff has been breaking them at the other, reaching her first junior slam final at the US Open aged just 13.

She won the French Open title last year and, on this evidence, she is more than ready to make a big impression in the senior game.

For Venus it must have been like facing a teenage version of herself as her opponent fired down serves over 110mph and scampered around the court with her long levers.

Gauff is already a terrific athlete and Williams was simply unable to hit through her. What was most impressive, though, was the way she constructed points, playing close to the lines but rarely too close and using angles to open up the court.

Williams saved three match points in the final game before creating one break point, which Gauff saved with a 108mph second serve. When her fourth opportunity came, she took it, then dropped to the court in disbelief.

"On my science test, I got a B," she said. "Today I'd give myself an A."