The 19-year-old defeated Belgian ninth seed David Goffin 7-5, 7-5, 6-3 to become the youngest player in the last-eight since Andy Roddick in 2001.
“Rafa is a real champion. I will try to do my best – I have nothing to lose,” said the world number 53.
Petra Kvitova established herself as a contender for what would be the most remarkable of titles after defeating Wimbledon champion Garbine Muguruza in the fourth round of the US Open.
It was the most significant match since Kvitova’s comeback from the horrendous hand injuries she suffered when she was stabbed by an intruder at her home last December.
And the Czech reminded everyone just what an unstoppable force she is in full flow with a stunning 7-6 (7/3) 6-3 victory over the clear title favourite.
Kvitova admitted to nerves in the final game, where she had to save three break points, roaring herself to victory.
“It was the kind of moment that I dream of to come and play again on the big stages against great players on the tour,” she said. “That was one of the motivations to be back.
“So probably in my mind was just there, thinking about it. I didn’t really play these kind of great players so far in the season when I came back. It was something really special for me.
“I knew how everything was just so tight and very close, every game that we played in the end of the match. I just knew it would be about a few points.”
This is only the second time Kvitova has made the quarter-finals at Flushing Meadows and she has never been further.
The 27-year-old, who next faces Venus Williams, insisted she will continue to play with no expectations but also without being surprised by what she can still produce.
She said: “I’m not thinking like that any more. I think maybe it’s a bad sign sometimes, that I should be more appreciating than I am probably.
“But sometimes I just really feel that the touch is there, the strength, the aggressive kind of game plan. It took me while to find it. Luckily I found it in a grand slam.
“The women’s race is still very, very open. Of course, Garbine was one of the favourites to win the title and be number one. I’m sorry, I’m not sorry I beat her. I’m still happy that I’m in the tournament. But anyone from the draw can win the title here.”
Muguruza was so confident, so assured after her brilliant summer and looked to have too much consistency for Kvitova when she eased into a 4-1 lead.
The turning point came in the next game. Muguruza had chances to go 5-1, could not take them, and slowly Kvitova began to turn the screw.
A missed volley and double fault cost Muguruza the tie-break and she could not turn the momentum back in her favour.
The 23-year-old could yet finish the tournament as world number one, with Elina Svitolina needing to reach the semi-finals or Karolina Pliskova the final to deny her.
And, whatever happens, Muguruza will leave New York in a positive frame of mind, saying: “I’m very happy with the tournament.
“Even though today didn’t go my way, I didn’t feel I did something wrong out there. I think she played very good. We all know she can play, finding the incredible shots and serve.
“Overall it’s a very good tournament for me. Not only a tournament, but the summer in general. I feel very happy. This match is just a match, but I’m happy with all the period that I’ve been playing.”
Muguruza buckled under the weight of expectation after winning her first grand slam title in Paris last summer but is embracing the pressure this time.
“I like it,” she said. “If people think I could be a good competitor there and go far, that’s fine. Of course, I feel these butterflies and things like this. But I go out there, I do my best, and that’s all.”
At the age of 37, Williams is having her most consistent season at grand slam level for 15 years.
After reaching the final of both the Australian Open and Wimbledon and the fourth round of the French Open, she made it an unhappy birthday for Carla Suarez Navarro with a 6-3 3-6 6-1 victory.
Williams has not won a grand slam title since 2008, while the second of her two US Open crowns came way back in 2001.
The American, like everyone in tennis, was shocked by Kvitova’s ordeal and has been inspired by her comeback.
“What she’s gone through is unimaginable, unreasonable,” said Williams.
“The world we live in is just shocking. So for her to be playing well is such a blessing. To be able to come out here and do what she needs to do, to clear her head, it’s such a beautiful thing to see.”
Maria Sharapova’s Grand Slam return after a 15-month doping ban ended in the US Open fourth round Sunday with the former world number one losing to Latvian 16th seed Anastasija Sevastova.
The 30-year-old Russian star, whose five Grand Slam titles include the 2006 US Open, fell 5-7, 6-4, 6-2 to Sevastova, who booked a Tuesday quarter-final matchup against American Sloane Stephens.
Sharapova, who returned to the tour in April after her suspension ended, had defeated world number two Simona Halep in the first round and was being spoken about as a potential title contender.
But despite pocketing the first set, her challenge fizzled out when she needed a medical timeout to treat a blister on her right hand.
She finished with 42 winners but 51 unforced errors against Sevastova, who also made the quarter-finals in 2016.
“Playing on Ashe stadium is an amazing atmosphere, every time. It’s fun to play here,” said 27-year-old Sevastova, who took victory on a fourth match point when Sharapova pushed a service return wide.
“The first set was very close. It could have gone either way. She played unbelievable throughout the first and second set and I just kept fighting, running for every ball.
“The emotions were high when I was 5-2 up in the final set. I wanted to close it so much.”