NEW YORK — Naomi Osaka and her smorgasbord of new fans saw her U.S. Open title defense fizzle Monday because of an ancient wrinkle of sports draws: the matchup problem. As Belinda Bencic appeared to give Osaka’s game a keen reading for the third time this year, it grew clear that Osaka’s opponents included, in ascending order, Osaka’s knee, Bencic’s know-how and the diabolical system that placed Bencic in ­Osaka’s draw neighborhood.

While Osaka’s 2019 season will always include her Australian Open title, her ascent to No. 1 and her widely revered turn of sportswomanship from Saturday night, her record this year against Bencic shouts 0-3 after Bencic’s 7-5, 6-4 win in the fourth round. That outcome in 97 well-played minutes made Bencic the second Swiss player within 15 hours to dismiss a No. 1 seed, after that old male warhorse Stan Wawrinka spent Sunday night surpassing Novak Djokovic.

Osaka was gone only about 40 hours after her moment of Saturday night, when she beat 15-year-old Floridian sensation Coco Gauff, 6-3, 6-0, then persuaded Gauff to stay with her untraditionally for the traditional on-court interview because she wanted Gauff to feel the fans’ appreciation.

Yet after the global response surprised her even with her notifications turned off, she came upon an opponent who had watched from the stands for Osaka-Gauff, who admired the gesture and who maybe even studied further the winner. Bencic’s show of expertise left Serena Williams, pursuing her record-tying 24th Grand Slam title, as the only remaining quarterfinalist with any Grand Slam singles championship, left No. 8 Williams and No. 5 Elina Svitolina as the only top-10 players still churning here, prevented any Osaka-Williams rematch of last year’s noisy final and left a reminder that the player ranked 12th in the world, Bencic, can menace.

In Indian Wells, Calif., in March, she bested Osaka, 6-3, 6-1.

In Madrid in May, she shook off an unfavorable match point and beat Osaka, 3-6, 6-2, 7-5.

By the time they got to New York in September, beneath a closed Arthur Ashe Stadium roof shielding them from downpours at high noon, Bencic seemed to play points as if a split-second prescient. That, mixed with a mere 12 unforced errors, made Bencic look just about ironclad.

“I think my game is very much on instinct,” she said, soon continuing with, “You have to react to it in seconds. I don’t know. It’s maybe just a feeling inside me. It’s not like I watch her games and I see, ‘She’s going cross-court all the time.’ It’s just where she stands, the angle of the ball, how fast is it, how much spin is there. I think you need to decide all this in seconds. I think it’s not the brain, but it’s just instinct.”

All that instinct left Osaka “not that mad at this” loss, of which the 21-year-old said, “I think she had, like, a specific plan that she wanted to execute.” Bencic executed it with reading skill that derives partly from childhood training, which began at the ripe age of 3 with Melanie Molitor, best known as the mother and coach to five-time Grand Slam champion Martina Hingis. By the time Bencic was a teenager, she occupied that wonderful, horrible zone of the prodigy, the kind of promising talent who eventually reaches 22 and says, as she did Monday, “People always think I’m older than I actually am.”

“I was really young when she was playing,” Bencic said of Hingis, whose Grand Slam titles came compressed between 1997 and 1999. “Obviously I knew who she was and what she has achieved. I think it was not necessary to study her game. I did everything on the practice the way I should.

“But I think with Melanie we didn’t try to, like, copy Martina’s game. We tried to make my own game. And obviously know there are similarities because that’s the way Melanie teaches, but it was about to make my own strengths and my own game style. I think I play, of course, a little bit different than Martina. I think she was even more skilled and smarter on the court and playing more chess. I think I have a little bit less maybe talent and touch than her but ­maybe a little more power.”

At 17, Bencic whisked through such bright lights as Angelique Kerber and Jelena Jankovic to the 2014 U.S. Open quarterfinals. Then she spent five years and 16 Grand Slam tournaments and umpteen injury recoveries seeking that stage again. She accessed it Monday when she served for the match, held her nerve and held at love, closing with a cunning serve up the middle that coaxed a sitter, which she blasted, and from which Osaka’s lunging reply never had any hope.

“I hurt my knee [last month] in Cincinnati, but it’s getting better,” Osaka said. “I don’t want to say that that’s the reason that I lost, because I obviously had played, like, three matches before this. Yeah, I just needed to take a painkiller.”

Oddly, she remains unbeaten in Grand Slam quarterfinals, semifinals and finals at 6-0. Yet she found this exit less dispiriting than others.

“In Wimbledon [a first-round loss], I walked out on you [reporters],” she said. “In Roland Garros [a third-round defeat], I came straight from the match, so I was all gross and I just wanted to get out of there. Obviously, as you can see, I took a shower.”

Everyone laughed, and she added: “Yeah, I feel like I’m more chill now. Because it sort of relates back to . . . I feel like I grew. I don’t feel like I put so much weight on one single match.”

In a season with some dips, she had learned it hadn’t helped to take herself too seriously. And she seemed clearheaded when she said: “It’s something that I’ve learned over the summer that, even if you aren’t playing your best, you’re going to play people who are going to play their best. You have to figure out how to win those matches.

“And it’s matches like that that are most important, because it really tests your character. So I think on that side I have a lot of growing up to do.”