Still only 17, she will be participating in the women's quarterfinals Tuesday, playing 39th-ranked Peng Shuai of China.
"It's insane," was the way Bencic put it.
Bencic has already beaten three seeded players - No. 6 Angelique Kerber, No. 9 Jelena Jankovic, No. 31 Kurumi Nara - along with past U.S. Open semifinalist Yanina Wickmayer and assured herself of moving into the WTA's top 50.
Bencic is the youngest quarterfinalist at Flushing Meadows since another player from Switzerland, Martina Hingis, was 16 in 1997. As it happens, Hingis is a mentor to Bencic, who is coached by Hingis' mother, Melanie Molitor.
"She's come a long way. I don't have to tell her that much. It's my mom who has done great work," Hingis said.
Did Hingis offer Bencic any advice about beating Peng?
Yes, Hingis replied, but added: "I'm not going to tell you, because it's going to be in the paper tomorrow."
Here are some other things to watch on Day 9 at the year's last Grand Slam tennis tournament:
FEDERER'S FOE: Roger Federer tries to get back to the U.S. Open quarterfinals after last year's surprising fourth-round exit, facing 17th-seeded Roberto Bautista Agut of Spain for the first time.
When Federer was asked to size up that Tuesday night matchup, he began by replying with a question of his own: "Didn't he win three different tournaments on three different surfaces this year?"
Well, close. Bautista Agut has won two titles on two surfaces in 2014 - at a Dutch tournament on grass in June, and at a German tournament on clay in July.
Aside from that, Federer provided quite a detailed scouting report on the guy.
"He's quick on his feet. He doesn't miss much. He's consistent. He's got a pretty good first serve. He's overall a solid player," Federer said. "I would assume he's fit, too, because he comes from the Spanish tennis school. ... They just know how to train hard. They never get tired. They're always ready to go. They have a good mental approach, point-for-point mentality."
"Then again," Federer continued, "he's not the typical Spaniard with a lot of topspin. I mean, he plays unbelievably flat actually, which is very surprising for a Spaniard."
Hmmm. Based on that lengthy description, makes one wonder whether Federer had a certain other Spaniard in mind - Rafael Nadal.
WOZNIACKI VS. ERRANI: A pair of past Grand Slam runners-up meet for a semifinal berth when No. 10 Caroline Wozniacki of Denmark faces No. 13 Sara Errani of Italy.
Wozniacki, a finalist at the 2009 U.S. Open, is coming off a fourth-round victory over five-time major champion Maria Sharapova. Errani, a finalist at the 2012 French Open, eliminated seven-time Grand Slam singles winner Venus Williams in the third round.
"It's going to be a completely different opponent," Wozniacki said, looking ahead to facing Errani after getting help from Sharapova's 21 first-set unforced errors. "She's not going to miss very much."
WILLIAMS SISTERS: Before Serena Williams plays Flavia Pennetta in the singles quarterfinals Wednesday, she'll pair up with older sister Venus in the double's quarterfinals as they seek their 14th Grand Slam title together - and first at Flushing Meadows since 2009.
Their opponents Tuesday are the fourth-seeded Russian duo of Ekaterina Makarova and Elena Vesnina, who won the 2013 French Open.
Entering the U.S. Open, the Williams sisters had played only three doubles matches all season, and one was a loss to Makarova and Vesnina at Dubai in February.