Gauff, the 15-year-old who became a household name for her exploits at Wimbledon earlier this year, was making her first appearance on court in the imposing Arthur Ashe Stadium.
Twenty-one-year-old Osaka, back at the scene of her dramatic triumph against Serena Williams 12 months ago, handled the occasion far better.
A Gauff double fault in her first service game gave her opponent a break and set the tone for a display peppered with too many unforced errors.
A pair of aces eventually saw the younger player hold, and she then broke back before further breaks of serve were exchanged, Osaka finally holding to take the set.
At the start of the second, audible groans went around Ashe when Gauff's double fault brought up 0-30, and a second handed another break to Osaka.
Three break points in the next game briefly raised hopes of a revival, but they were quickly snuffed out by Osaka's booming groundstrokes.
It was all over when a Gauff forehand went long, and Osaka rushed to console the teenager.
Gauff was persuaded by her opponent to stay for the courtside interview, and said: "She told me I did amazing.
"She said would I do the interview, I said 'no I'm going to cry', but she encouraged me to do it.
"It was amazing, I'm going to learn a lot from this match. She's been so sweet to me."
Osaka took it upon herself to speak to Gauff in the locker room earlier in the week. But she said: "I don't think I'm a mentor."
She added: "I think this is the most focused I've been since the Australian Open. It was super fun. The energy was crazy, even if it really wasn't for me."
Earlier, qualifier Taylor Townsend continued her remarkable US Open run with victory over Romanian Sorana Cirstea.
The American world number 116, who stunned Wimbledon champion Simona Halep in round three, beat Cirstea 7-5 6-2.
Townsend will face Canadian 15th seed Bianca Andreescu in the fourth round.
Andreescu defeated Caroline Wozniacki, the 19th seed, 6-4 6-4.
The 19-year-old Andreescu looks a real threat at Flushing Meadows this year and Wozniacki, twice a US Open runner-up, said: "She's playing very well and mixing up the pace. She has a lot of shots in her game that she can pull out.
"I think the one that I can most compare her game to would probably be Kim Clijsters, back in the day.
"I think because she moves well and she can stretch out and get to some balls and also play aggressive and using the angles.
"Everyone has their own style but for me, playing her, it a little bit brings me back to when I played Kim."
Germany's Julia Goerges pulled off a surprise by knocking out seventh seed Kiki Bertens.
Goerges, seeded 26, needed five match points but eventually got over the line 6-2 6-3.
American wild card Kim Ahn beat former French Open champion Jelena Ostapenko 6-3 7-5.
