The 15-year-old was bidding to become the youngest player to reach a grand slam quarter-final for 15 years, and she was one set away when she took the opener on a packed Melbourne Arena.
But 14th seed Kenin had other ideas, eventually wearing down Gauff in a 6-7 (5) 6-3 6-0 victory.
Gauff’s victory over defending champion Naomi Osaka was on paper certainly the best of her fledgling career but, so poor had the Japanese been, it was difficult to gauge how well the teenager had actually played.
Kenin, a rising star herself at 21, made Gauff play a lot more balls and solve different problems and, if she can maintain the level she showed in the first set, then it is clear the teenager will soon be challenging for the biggest titles.
Gauff said: “The thing I’m most proud of is how I handled it on the court. Even though today I lost a set 6-0, I was still believing I could win it.
“I don’t think I showed any negative emotion too much in the match. I just tried my best. What surprised me is how calm I was going into all these matches. I wasn’t really nervous. I’m happy that I’m not letting the moment seem too big than what it is.”
Gauff was in tears at the end, but she said: “I had a lot of fun. The crowd was really rooting for me. I had a great tournament. I was disappointed that I lost obviously.”
Under WTA rules, she can only play one more tournament before she turns 16 in March, which will be the BNP Paribas Open in Indian Wells.
Kenin’s climb up the ranking has come without the attention of Gauff’s and she will play in the last eight of a grand slam for the first time.
She will next face Tunisia’s Ons Jabeur, who continued her best slam run by beating Serena Williams’s conqueror Wang Qiang 7-6 (4) 6-1 to become the first Arab woman to reach the quarter-finals of a slam.
The 25-year-old, who is ranked 78, has beaten Johanna Konta, Caroline Garcia, Caroline Wozniacki in the Dane’s final match and now Wang.
Top seed Ashleigh Barty avoided an Australia Day upset, avenging her Wimbledon loss last summer by seeing off American Alison Riske 6-3 1-6 6-4. Next up for Barty is another rematch, this time with Petra Kvitova, who beat her in the quarter-finals last year to end hopes of a home winner.
Kvitova, who lost in the final to Naomi Osaka, also came through a battle, recovering from a set down to defeat Greece’s Maria Sakkari 6-7 (4) 6-3 6-2.