Osaka, 21, was broken late in the opening set and then again in the fifth game of the second under the Arthur Ashe Stadium roof at Flushing Meadows.
Japan’s Osaka will lose her world number one ranking, with Ashleigh Barty of Australia to return to the top spot.
Bencic, the 13th seed, will play Donna Vekic in the quarter-finals.
The Croat, seeded 23rd, saved a match point as she beat Germany’s 26th seed Julia Gorges 6-7 (5-7) 7-5 6-3 in two hours and 42 minutes on Louis Armstrong Stadium.
For Bencic, 22, it is her second appearance in the quarter-finals after also making the last eight in 2014 as a 17-year-old.
She has now beaten Osaka three times this year after previous victories in Indian Wells and Madrid.
“I was so excited to come on the court, the challenge cannot be bigger – Naomi Osaka is a great player and won the US Open last year,” said Bencic. “I had to be on top of my game and am really pleased with how I played.
“She has a lot of power, I was just trying to play it a little bit like chess, anticipate and make a tactic on the court.”
Osaka, who beat Serena Williams in last year’s final for her maiden Grand Slam title, started off badly as she lost her serve at the first opportunity and had to save two break points to avoid going 3-0 down.
She then fought back with a break before Bencic took the decisive break in the 11th game and then served out the set.
In the second set, an Osaka double fault gifted Bencic another break and the Swiss player took the final game of the match with a service hold to love.
After winning the Australian Open in January for her second Grand Slam, Osaka became the world number one, a position she held until June when Barty took over.
Osaka returned to the top eight weeks later but Barty will become number one again, despite losing in the last 16 to China’s Qiang Wang on Sunday.
Vekic comes back from brink to beat Gorges
Bencic’s quarter-final opponent will be 23-year-old Vekic, who is through to the last eight of a Grand Slam for the first time after a superb recovery against Gorges.
Germany’s Gorges served for the match when leading 5-4 in the second set but appeared overcome with nerves, coughing up three double faults among a series of errors.
She did have a match point but netted a forehand and when a serve-volley went long, Vekic was back at 5-5. The Croat then broke again in Gorges’ next service game to take the second set.
A single break in the decider left Vekic serving for the match at 5-3 and she had to save two break points before a Gorges smash went over the baseline to give her the victory.
“She was serving for the match, had match points but I just kept fighting and believing I could win,” said Vekic.
“I was just trying to get a return in the court, she was serving amazing, but I felt confident in the rallies.”
On facing Bencic, Vekic added: “She is a really good friend of mine, we practise together often and know each other’s game pretty well. She’s one of the best players this year.”
source:bbc
