Peng joins two-time Grand Slam winner Li Na and Zheng Jie as the only Chinese to reach the final four of a Grand Slam — and she did it in her 37th appearance in a major tournament.
Peng, who has reached the semifinals without dropping a set, was in charge from the beginning against Bencic, the unseeded 17-year-old who was already the youngest US Open quarterfinalist since Martina Hingis won the title at 16 in 1997.
Peng fended off two break points in her opening service game and didn't face another in the 64-minute match.
She broke Bencic twice in the first set, and seized a 4-0 lead with two breaks of serve in the second.
Bencic, at a loss, was warned for receiving coaching.
She argued, but as she returned to the baseline to resume play couldn't resist sliding her eyes toward her box.
Although Peng, ranked 39th in the world, was in her first Grand Slam quarterfinal at last, the 28-year-old had plenty of big-match experience to draw on.
In February, she became the first Chinese player to reach number one in the world when she went top of the doubles charts thanks to her success with Taiwan partner Hsieh Su-Wei.
The duo won their second Grand Slam doubles title at the French Open this year.
Peng, who ousted fourth-seeded Pole Agnieszka Radwanska, 28th-seeded Roberta Vinci and 14th-seeded Lucie Safarova to reach the quarters, was to face either former world number one Caroline Wozniacki or 13th-seeded Italian Sara Errani for a place in the championship match.