Peng, 28, delivered a master lesson to the 17-year-old Bencic on Arthur Ashe Stadium court in a battle of unseeded players, winning the groundstroke rallies and unleashing passing shot winners after luring the Swiss to the net with short balls.
World number one-ranked doubles player Shuai, whose best previous singles result in 36 grand slams was to the fourth-round, used her two-fisted groundstrokes to register 24 winners and seven unforced errors in a virtuoso performance.
The Chinese will play either former world number one Caroline Wozniacki, the 10th seed from Denmark, or Italian 13th seed Sara Errani in the semi-finals.
(Reporting by Larry Fine; Editing by Frank Pingue)
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