Peng, 28, delivered a master lesson to the 17-year-old Bencic in an unlikely quarter-final between unseeded players, winning the groundstroke rallies and unleashing pinpoint passing shot winners after luring the Swiss to the net with short balls.
After 2013 junior world number one Bencic netted a backhand for her 19th unforced error on the first match point of the 64-minute clash, Peng pumped her fist in exaltation, but later was at a loss of words.
Asked about reaching her first grand slam singles semi-final in her 37th attempt in a major, an emotional Peng took a few moments to collect herself.
“This is amazing time for me,” said Peng, ranked world number one in doubles, but whose best singles result in 36 previous slams was to the fourth round.
“A lot of tennis. It’s a long time, the career. It’s tough sometimes. I’m thinking to give up and stop play because I don’t know if I can make it or not.”
Peng has won 16 doubles titles, most recently claiming the French Open title with Hsieh Su-wei, but has yet to win a tour singles title.
“I really thank my coach, my parents. They always tell me to fight and keep going and never ever give up. And this today was coming,” Peng said.
Peng and Bencic both carved out surprising paths to the quarter-finals.
The 39th-ranked Chinese rattled off three impressive upsets in a row from the second round, ousting fourth seed Agnieszka Radwanska, 28th seed Roberta Vinci and 14th-seeded Lucie Safarova.
Big-hitting Bencic, last year’s French and Wimbledon junior champion who is ranked 58th, also upset 31st seed Kurumi Nara, sixth seed Angelique Kerber and ninth-seeded Jelena Jankovic.
Bencic was the youngest player to reach the U.S. Open quarters since compatriot Martina Hingis in 1997. Hingis, is a friend and practice partner, whose mother Melanie Molitor coaches the up-and-coming Swiss player.
The teenager had shown impressive composure in her run to the quarters, but the precision brilliance of Peng frustrated her.
Bencic showed her frustration by muttering angrily at herself, and swiping at the air with her racket. After falling behind 2-0 in the second set, she bickered with the umpire after being issued a coaching warning.
Peng, meanwhile, stayed focussed on business.
The Chinese winner was never threatened in the one-sided contest, winning 54 points to 36, ripping 24 winners to double Bencic’s total, while committing only seven errors in a virtuoso performance.
Peng will play either former world number one Caroline Wozniacki, the 10th seed from Denmark, or Italian 13th seed Sara Errani in the semi-finals.
Top-seeded two-time defending champion Serena Williams used a medical timeout to have her right foot and ankle re-taped during the second set of her quarter-final doubles match against Russians Ekaterina Makarova and Elena Vesnina.
Williams, playing with her sister Venus, appeared to be all right after timeout but it proved to be a disappointing performance.
The fourth-seeded Russians went on to win 7-6 (5) 6-4, advancing to the semi-finals after Serena double-faulted on the last two points of the match.
(Editing by Frank Pingue)