At the 1997 United States Open, Melanie Molitor coached her 16-year-old daughter, Martina Hingis, to her third Grand Slam title. Now, Molitor has led Belinda Bencic, 17, into the fourth round of the tournament.

Bencic scored the first top-10 victory of her career Friday, beating sixth-seeded Angelique Kerber, 6-2, 7-5, to reach the second week. Bencic will make her debut in Arthur Ashe Stadium in Sunday’s night session, taking on ninth-seeded Jelena Jankovic, a Serbian veteran 12 years her senior.

“It feels great,” Bencic said after beating Kerber. “It was always my dream to beat a top-10 player and to play on a big court. So I’m really satisfied with how I played, but now I cannot be happy. I will be more motivated to work even harder.”

Bencic is the latest in an unlikely stream of elite Swiss tennis players in recent decades, started by Hingis and continued on the men’s side by Roger Federer and Stan Wawrinka.

“I don’t know why we have so many good players,” Bencic said of Switzerland. “Maybe it’s in the chocolate or something?”

Though this is her biggest achievement so far on the professional level, Bencic was a dominant force last year as a junior, winning the French Open and Wimbledon. Her rise through the professional ranks has been smooth as well. She started the year ranked 212th and has steadily climbed to her current ranking, 58th.

“The juniors gave me a lot of confidence, and I have learned winning,” she said. “I can take this experience with me, and I’m not afraid when it’s getting tight or something.”

She recently told Sports Illustrated that she checks the WTA and the International Tennis Federation websites when she gets up in the morning. She still keeps tabs not only on her professional peers but also on the juniors in the pipeline, including CiCi Bellis, the 15-year-old American who won her first-round match at this year’s tournament.

“I think it’s great that a lot of junior players are coming up,” Bencic said. “CiCi Bellis as well, she did a great job. I think it’s great for women’s tennis to see the fresh faces coming up. It’s really interesting, and mixes up the draw a little bit.”

Hingis beat Venus Williams, then 17, in the 1997 U.S. Open final, but teenage success has been rare in women’s tennis in recent years.

Hingis, who is competing in the women’s doubles event here, said that although she saw similarities between her game and Bencic’s, there were differences as well.

“The technique, my mom puts a lot of attention to that,” she said Saturday. “So the game, I mean, she’s got a great backhand as well. But also she’s stronger, so she can work with other weapons than I had. I mean, maybe I was more maybe a little better mover, but when she hits a shot it can be a winner. Like she’s hitting a lot more winners than did I. So it’s different a little bit.”

Molitor does not travel with Bencic, leaving her under the watchful eye of family. Bencic’s parents, like Molitor, were Slovak immigrants to Switzerland. Her father, Ivan, has been omnipresent through her rise this year, acting as a protective shadow as she moves up in a world that can be destructive to teen prodigies.

Ivan Bencic said one of his duties during his daughter’s breakout year had been to keep her from getting carried away with her success.

“My job is after to bring her down a little bit, to stay on the ground,” he said. “We will see; she still has to learn. She’s very intelligent; she understands. She has emotions, but it’s been O.K. until now. We can handle it.”

While her father tries to keep Bencic tethered, Hingis sees no limit for her.

“I think there is huge potential for her,” she said. “I mean, I definitely think she can be top five. She’s on the way to get there. How far, it’s up to her. You know, nobody can play the matches for her and win matches, win the tournaments. But she showed yesterday that she can win a big match when she has to. Hopefully there will be more opportunities in the near future. Maybe here.”

While describing herself as funny and friendly, Bencic does not hide her hunger.

“I always want to win in everything,” she said. “And I’m really ambitious.”An earlier version of a summary with this article misidentified the player who has steadily risen through the professional ranks this year. She is Belinda Bencic, not Melanie Molitor, her coach.