Four-time grand slam champion Osaka showed flashes of her old brilliance as she took control of the match from the start, while the 2023 champion Gauff struggled with her forehand and serve.
The result carried Osaka into the Flushing Meadows quarter-finals for the first time in five years and she will next play 11th seed Karolina Muchova.
Monday's showdown marked the first time that the two fan favourites met in New York since their memorable 2019 tussle when the then 15-year-old Gauff lost to the Osaka.
For Osaka, this marks a real return to her best play since she came back to the tour after a 17-month maternity leave. Her child, Shai, was born in July 2023.
"I'm a little sensitive and I don't want to cry, but honestly, I just had so much fun out here," said Osaka, whose last major was the 2021 Australian Open.
"I was in the stands like two months after I gave birth to my daughter, watching Coco. I just really wanted an opportunity to come out here and play.
"This is my favourite court in the world, and it means so much for me to be back here."
Muchova beat 27th seed Marta Kostyuk of Ukraine in a two-hour 53-minute epic 6-3 6-7 (0-7) 6-3, continuing her run of three-set matches in New York.
The Czech made the semi-finals here in 2023 and 2024.
Elsewhere, a laser-focused Iga Swiatek barely broke sweat as the former US Open champion methodically dismantled Russian 13th seed Ekaterina Alexandrova 6-3 6-1 and booked her return to the quarters.
The 24-year-old's crushing win on Louis Armstrong Stadium meant that she became the youngest woman to reach at least the last eight of all four grand slams in a single season since 18-year-old Maria Sharapova managed the feat in 2005.
"In the beginning I felt like she played fast and the court is different. I wanted to find my rhythm afterwards and I was in my bubble," the world No.2 said after reaching her 13th major quarter-final.
Six-times major winner Swiatek is seeking to become the first woman since Serena Williams in 2012 to win Wimbledon and the US Open in the same year.
Up next for the Pole is American eighth seed Amanda Anisimova, whom she thrashed 6-0 6-0 in this year's Wimbledon final.
The 24-year-old, who had already defeated Australians Kimberly Birrell and Maya Joint in New York, needed only 76 minutes to eliminate  Brazilian 18th seed Beatriz Haddad Maia, 6-0 6-3.
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