NEW YORK -- Back in January, Coco Gauff lost to Madison Keys in Adelaide.

“I learned a lot from that match,” Gauff told reporters earlier this week. “In the beginning of the year I feel like in general, I wasn’t in a good head space, I wasn’t confident in my tennis. I feel like now I’m really confident in my tennis. 

“I think my serve is a lot better. I’m winning a lot of first-serve points. Forehand has improved a lot. Return has improved. Also, just my mentality on the court.”

Coco Gauff

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That’s a lot of improvement -- in a span of only eight months -- but this 18-year-old is blasting through a learning curve that typically takes years and years. There was more progress Friday at the US Open, when Gauff beat Keys 6-2, 6-3 in a third-round match.

It was clean, comprehensive and thoroughly cerebral. After the last point, Gauff screamed -- more animated than usual -- and pointed at her head.

The No.12 seed meets Zhang Shuai, a winner against Rebecca Marino, in a fourth-round match Sunday.

Playing in her third US Open, Gauff is into the second week for the first time. This had been the only major event where that hadn’t happened. Overall, this was her sixth victory at her home Grand Slam -- a total she matched earlier this year in a single fortnight with a run to the final at Roland Garros.

Keys, who reached the finals here in 2017, is a classic hard-court power player. She had recorded the most aces of any woman on hard courts this year, but Gauff held her own in those power categories. At the same time, Gauff -- among the quickest players on the WTA Hologic Tour -- was able to frustrate Keys with nearly impenetrable defense.

In a second-round match against Elena-Gabriela Ruse, Gauff knocked off a 128 mph serve. It was the second-fastest serve by a woman in US Open history -- and it was only one mile-per-hour behind the best efforts of top seed Daniil Medvedev, Stefanos Tsitsipas and Dominic Thiem.

Gauff saw the number on the scoreboard.

“I looked at it and I was like, `Whoa,’” Gauff told reporters later. “Yeah, I don’t know how that happened. It didn’t feel like I hit it that hard. I kind of looked at [Ruse] after. She was laughing at her box. I was like, ‘I don’t know what’s going on either.’”

Going forward, what’s going on is Gauff. She’s already a handful, but when you add her bigger and better serve to the stew, she’s becoming very, very tough to beat.