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.
Belgian 25th seed Elise Mertens breezed past American qualifier Kristie Ahn 6-1 6-1 in 66 minutes and will play Canadian 15th seed Bianca Andreescu next.
Andreescu, 19, beat American Taylor Townsend 6-1 4-6 6-2 to reach her first grand slam quarter-final.
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, Osaka, who later said she had been struggling with a knee injury, double-faulted to gift Bencic another break and the Swiss player took the final game of the match with a service hold to love. –BBC
