Belinda Bencic was sitting in Arthur Ashe stadium on Saturday night as Naomi Osaka and Coco Gauff battled each other and then cried together. Everyone else was there to see the show and the hype, but Bencic has already experienced enough hype to last a lifetime. She scouted her next match, then quietly departed without a word on social media. On Monday, her preparations proved sufficient as Bencic ended Naomi Osaka’s US Open defence with a 7-5, 6-3 win in the fourth round.

Osaka and Bencic were born in 1997 but it is difficult to think of two more different paths to this moment. While Osaka forewent junior tennis and arrived on the big stages fully formed, seemingly out of nowhere, Bencic was perhaps even more prodigious than Gauff. As a junior she won two grand slam titles and became junior number one, slaying all opposition in a 39-match winning streak.

When Bencic and Osaka played for the first time six years ago, the Swiss was shocked. “She totally killed me,” said Bencic, smiling. “I didn’t know her before but she had so much power already back then and me, like, none.”

Johanna Konta can vanquish self-doubt and win US Open, says coach Read more

At 17 years old Bencic was ready, storming to the quarter-finals of the 2014 US Open. While Bencic won her first cool $370,250, Osaka was ranked outside the top 250, playing in tournaments with a total purse of $25k. In 2015 she recovered from a set down to defeat Serena Williams en route to her big title in Toronto. As she celebrated her delirious win over Williams, fireworks burst triumphantly into the night sky from nearby. It seemed the perfect signal of her arrival at the top of the sport.

Instead Bencic would spend much of the following three years struggling back from countless injuries, including surgery to her left wrist. Whenever she looked ready to take on the world, another injury would scupper her chances. As Bencic struggled, she watched as Osaka found her feet and soared to the top of the sport.

This year Bencic has returned stronger, fitter and with a better understanding of what she is trying to do. Ranked 45th, her form since has taken her back into the top 15. Bencic arrived in New York with a 2-0 record against Osaka this year and she always seemed to save her best for the No 1.

Bencic’s performance on Monday was a thing of wonder. She immediately put pressure on Osaka by standing on top of the baseline, redirecting her pace and rushing her with early, precise ball striking.

While Osaka was inspired by Serena Williams, Bencic’s game was built brick by brick by the mother of Williams’ bitter rival, Martina Hingis. As with her daughter, Melanie Molitor taught Bencic to see tennis as a chessboard and to outsmart her opponents instead of hitting them off the court.

“I don’t have the biggest power, don’t have the most winners or most aces,” said Bencic. “But I can really read the opponent’s game well. I definitely try to do that against anyone, not only against her.”

Staring down an early 0-2 deficit, Osaka saved four break points and the first set became an electric, high-quality battle. Bencic was dominant throughout the rallies while Osaka would constantly find an ace and a big serve to keep herself in contention.

Both players held until the pressure at 5-5, 30-30, Bencic slotted a backhand winner to break, before comfortably serving out the set.

After a series of early holds in the second set Bencic’s awareness secured the crucial break. At 2-2, 0-30, Osaka perfectly set up a short ball and then swept to the net to finish the point with a backhand drive volley. Bencic was far out of the court, the point seemingly over, but she held her ground instead of running and anticipated that Osaka would hit straight back to her. When she did, Bencic slotted a backhand winner down the line. On the next point Osaka double-faulted and her fate was sealed.

“My game is very much on instinct,” said Bencic. “You have to react to it in seconds. It’s maybe just a feeling inside me.”

Bencic’s serve had never been big, yet she finished with 82% first-serve points won. Her game is not built to overpower opponents but she redirected Osaka’s pace so well that she finished with 29 winners to 12 unforced errors.

“I learned so many things,” said Bencic. “Everyone expected [my career] to go just up. That’s not how tennis goes. All true athletes have to overcome obstacles, injuries, just tough times. It made me a stronger person, better player.”

Bencic will face the 23rd seed, Donna Vekic, in the quarter-final, who overcame the 26th seed, Julia Görges, 6-7(5), 7-5, 6-3.