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 her serve.
The result carried Osaka into the Flushing Meadows quarter-finals for the first time in five years and she will next play either Czech 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 returned 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," Osaka told the crowd. "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.
Earlier, 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 quarter-finals.
The 24-year-old's crushing win on Louis Armstrong Stadium meant that she became the youngest woman to reach at least the quarter-finals of all four Grand Slams in a single season since 18-year-old Maria Sharapova managed the feat in 2005.
Swiatek was typing away furiously on her phone as she waited for her on-court interview afterwards and said she was sending a message to her coach Wim Fissette.
"I asked him to book a practice court for 10 minutes, if possible," the world No.2 said, before she explained what worked well in helping her reach her 13th major quarter-final.
"I would say the intensity and focus. 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.
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 either American eighth seed Amanda Anisimova, who she thrashed 6-0 6-0 in this year's Wimbledon final, or Brazilian 18th seed Beatriz Haddad Maia.
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