NEW YORK—Patience is a virtue, unless you've endured a decade toiling for an elusive Grand Slam semifinal. When Peng Shuai took her double-fisted shot at a major breakthrough, there was no time for tolerance.

Contesting her first major quarterfinal in her 37th career Grand Slam appearance, Peng wasn't interested in playing the waiting game. Serving with authority and stinging the first strike, Peng schooled talented Swiss teenager Belinda Bencic, 6-2, 6-1, to reach her first final four at a major.

This was a 64-minute tutorial in leveraging aggressive court positioning into sharp angles to shred an inexperienced opponent. Exposing the 17-year-old's struggles with the wide ball, Peng doubled her opponent in winners (24 to 12), committed far fewer errors (seven to 19), and exuded a calm but commanding disposition for much of the day.

It all stemmed from serve. Launching herself up on serve, the 28-year-old Chinese erased a pair of break points with an ace wide and a slider down the middle, eventually holding for 2-1. Those were the only break points Peng faced all day. Her toughest hold of the match ignited a run where she ripped through 10 of the next 11 games.

Because Peng often plays so flat, conventional wisdom dictates creating sharper angles to drag her wide and force her to take one hand off the racquet. Bencic did exactly that with a severe backhand angle, but Peng ran it down, poking a one-handed answer in the fourth game. She broke for 3-1 when Bencic dribbled a backhand off the tape.

When Bencic attacked behind a swing volley, Peng calmly stood her ground and buried a cross-court backhand to end the 35-minute opener with a bang. The Roland Garros doubles champion played cleaner tennis, hitting 15 winners against four unforced errors.

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U.S. Open: Peng d. Bencic

U.S. Open: Peng d. Bencic

Coached by Melanie Molitor, mother and former coach of Hall of Famer Martina Hingis, Bencic's impeccable timing, ability to strike on the rise, court sense, and Hingis-esque two-handed backhand are all assets. "She's got a great backhand, but also she's stronger, so she can work with other weapons that I had," said Hingis, who was wearing an over-sized white floppy hat in Bencic's support box today. "When she hits a shot it can be a winner. She's hitting a lot more winners than I did."

Deconstructing two former U.S. Open semifinalists—Yanina Wickmayer and Angelique Kerber—before defeating 2008 finalist Jelena Jankovic, Bencic barely looked stressed surging into her first quarterfinal in just her fourth major. Bencic is more powerful than her mentor, but not as quick around the court as Hingis was, and her anticipation isn't quite as sharp. On key points, Peng made Bencic hit on the run; the youngster's accuracy wavered and game withered on the hottest day of the summer.

When Bencic buried a forehand into net, the world No. 39 broke for a 2-0 second-set lead. The youngest Grand Slam quarterfinalist since Nicole Vaidisova at the 2006 French Open, Bencic lost her focus briefly when she was hit with a coaching violation warning. "It's 6-2, 2-0 and you give me a coaching violation?" an incredulous Bencic asked in response.

Peng, who showed variety playing the drop shot and even a soaring lob winner, continued to coax errors, rolling out to a 5-0 lead until Bencic held at love. On the opening day for many area schools, the former world No. 1 doubles player issued early dismissal. She's reached the semis without surrendering a set. Peng, who was emotional in her post-match interview, will face either Caroline Wozniacki or Sara Errani for a spot in Sunday's final.