The loss marks the end of an incredible run for Wozniacki as she returned to a Grand Slam tournament for the first time since the 2020 Australian Open.
Wozniacki retired three years ago to start a family and was heavily pregnant with her second child during last year's US Open.
However, she returned to the WTA Tour last month, with Gauff remarking it is like the Dane "never left".
"The level that she's played today is really amazing," Gauff said.
"She's been an inspiration for me growing up."
The former world number one - a two-time US Open runner-up - said afterwards she was exactly where she wants to be.
"There's a lot of positives to take with me going forward. I'm on the right track," Wozniacki said.
"I'm finding my form, I'm finding my feet. I'm excited to take on more events and more players."
Elsewhere on Sunday, 10th seed Karolina Muchova set up a quarter-final encounter with Sorana Cirstea of Romania after defeating China's Wang Xinyu 6-3 5-7 6-1.
For world number 30 Cirstea, who beat Switzerland's Belinda Bencic 6-3 6-3, it will be a first appearance in the last eight of a Grand Slam since the 2009 French Open.
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