Coco Gauff shows how far she's come in Australian Open win over Venus Williams

Coco tops Venus for first career win at Australian Open (2:31)

Coco Gauff takes down Venus Williams in the first round in straight sets, 7-6, 6-3, for her first career win at the Australian Open. (2:31)

MELBOURNE, Australia -- When Coco Gauff beat Venus Williams at Wimbledon last summer, it was a huge shock -- the 38-year-old knocked off by an almost unknown 15-year-old on her favorite surface in the hallowed place where Williams had been the queen of grass five times.

But seven months is a lifetime for a teenager. So when Gauff repeated her victory over Williams at the Australian Open on Monday, this time winning 7-6, 6-3, it was expected. Gauff showed everyone just how far she has come since she burst onto the scene by reaching the last 16 at Wimbledon last summer.

Her maturity is remarkable. Here was Williams, now 39 and playing in Australia for the 20th time, rattled, exasperated, furious at her mistakes, unable to cover the court the way she once did, unable to penetrate holes in the defense of Gauff, whose athleticism and movement resemble Venus at her best.

At the other end, Gauff was problem-solving, working out what she needed to do and how to do it to stave off a comeback and get over the line. Not many 15-year-olds can do that, but this is no ordinary 15-year-old.

"She clearly wants it, works very hard, is extremely mature for her age," Williams said. "I think the sky's the limit for her."

When you're 15, improvement often comes in chunks; one minute your serve is impressive but erratic, the next it's a weapon -- first and second serve. One minute the technique on your forehand is being questioned, the next you're ripping winners with it.

In seven months, Gauff has improved physically, mentally and emotionally.

"I feel like my mindset has changed since the US Open," she said. "US Open, I feel like I was on edge every match just because everyone was talking about US Open before Wimbledon even ended. So I knew that was the next thing.

"I guess I came to the realization that I need to play my game, not worry about what people think of me. At the end of the day, I did have three good matches, both US Open and Wimbledon. I still have a lot more to, I guess, become like one of those big names. I feel like I still have a lot to improve."

Figuring things out in the middle of a match is not easy for anyone, let alone someone playing in the main draw at the Australian Open for the first time. But Gauff, already ranked 67th and heading higher soon, looked more like a Grand Slam champion than Williams.

"I think last time [she played Williams], even though I still think I played well last time, I think I was just trying to let her miss," Gauff said. "I knew I had to be more aggressive this time. I think I resorted back to trying to make her miss this time, [but] once I figured that wasn't working out, I knew I had to get back to being aggressive."

It's only two years since Williams reached the final in Melbourne and then again at Wimbledon. But at 39, maybe time is finally getting the better of her. Her movement was labored, especially to her backhand side, perhaps affected by the setback she cited for pulling out of Brisbane earlier this month. Although she battled and improved, it was her face, usually a picture of calm, that gave her true feelings away. It can't have been pleasant.

Gauff plays Barbora Strycova of the Czech Republic next, and the defending champion, Naomi Osaka, is likely to be waiting in Round 3. Asked if she was on a mission, Gauff said her mission is to be the greatest. And though she respects everyone, she is afraid of no one. It shows.

"I believe I can beat anyone," she said. "If it happens, I don't know. But I think that's almost every player's mentality, I feel like. The ones who are the great ones, they don't really fear anyone. You respect your opponent, but you can't go into the match fearing someone, because then you're going to lose, and I don't want to lose."

Williams was a little sketchy about her future commitments, and it is possible that Melbourne may have seen her for the last time, with the Olympics in Tokyo a potential end point should she feel like she's had enough after more than two decades on tour.

Gauff, though, is the future and quickly becoming the present.

"She played well," Williams said. "Just played very focused and put a lot of balls in the court. That's what you have to do. She'll play well the rest of the event."