On one of the several tumultuous days at this Australian Open, Chris Evert, perhaps the most perceptive of the former champions with access to a TV microphone, said: “Coco has arrived. We need that shot in the arm and we need some new blood in the women’s game.”

The American, who won 18 of her 34 grand slam singles finals, was talking about her 15-year-old compatriot, Coco Gauff, who had already put Venus Williams out of a slam in the first round for the second time in seven months, and had then beaten the defending champion, Naomi Osaka. Tennis was ready to crown its new princess.

Sofia Kenin battles back to beat Garbiñe Muguruza in Australian Open final Read more

Sofia Kenin was not quite so ready. The 21-year-old American, seeded 14th, might have reckoned there would be more noise attending her own progress, as she worked her way into the fourth round past two qualifiers and the unseeded Shuai Zhang without dropping a set.

There she looked across the net at Gauff, the player nearly everyone wanted to embrace as the next big prospect, an articulate and thoughtful teenager, respectful of her peers and the history of the game, and owner of a game that combined exquisite touch and growing power.

Kenin, it was said, lacked pop on her serve, especially if her first effort did not land, and her volleying needed work. But she beat Gauff, whom she likes, in three sets, the last without conceding a game. She found a way. Now they began to talk about the daughter of impoverished immigrants, about her father and coach, Alex, who had arrived in the United States from Russia with just $300 in his pocket, three months after she was born, and occupied the front row of her players’ box all fortnight like some knowing old party apparatchik.

Now Sofia – or Sonia, as he calls her – was going to pay him back, big time. In the quarters, she beat the unheralded Tunisian, Ons Jabeur, who had done some giant-killing of her own in beating Johanna Konta, the two Carolines – Garcia and Wozniacki – and the 27th seed, Wang Qiang. She fell to Kenin in straight sets. As did the world No 1 and home favourite, Ashleigh Barty. The clamour for the American with no discernibly big weapons but a huge fighting spirit began to grow.

Facebook Twitter Pinterest Sofia Kenin is congratulated by her father and mentor Alexander Kenin after beating Garbiñe Muguruza 4-6, 6-2, 6-2 in the Australian Open final. Photograph: Fiona Hamilton/HANDOUT/EPA

On Saturday, it appeared her run to glory, in her first slam final, might shudder to a halt when Garbiñe Muguruza, the double-slam champion, won the first set. Yet again, Kenin found a way. In just over two hours on Rod Laver Arena she ground down the experienced Spaniard 4-6, 6-2, 6-2.

Evert, who has known Kenin since she was six and watched her grow up in Florida, a shy but determined young player, said: “Sofia has been undervalued and she has been overshadowed by a lot of the American power players. But now America knows her and what she has. They know she is a champion.”

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She is also the new American No 1 – eclipsing Serena Williams – and the world No 7. She is moving comfortably in space occupied by Gauff, Osaka, Barty, Bianca Andreescu and Simona Halep. She is a threat to all of them.

Evert said on ESPN: “We saw it in her semi-final against Ash Barty, the same thing. When she was in trouble, when her back was against the wall, she came up with these shots. Champions do that and she has it. It is innate and I think a lot of it is just the hunger to win. It wasn’t about the power. It was how she hit the corners and her choice of shots. And her variety of shot, her drop shots. She served really well. She can still improve. She can still volley [better]. She can still improve that serve. A little bit of fitness. She is going to keep going up in the rankings.”

Kenin, who beat Serena Williams in the third round of the 2019 French Open and has twice reached round two at Wimbledon, will look towards Europe when the dust settles.

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Sofia Kenin, right, is embraced by Coco Gauff after beating her much-vaunted compatriot, widely seen as the next big prospect in women’s tennis, in the fourth round. Photograph: Andy Brownbill/AP

“Wimbledon is such a tradition,” she said. “You really feel it there. I love coming back, I love the people; the crowd is so fun.”

She appreciated that her parents struggled in Russia. “My dad has told me that it was a tough time for them. They didn’t have that much when they came to the States. They wanted to give me the American dream. I am really thankful. Without them, I wouldn’t be where I am today.

“Some people didn’t really believe in me. They turned me down and said I wouldn’t make it or I was too small. We never took that seriously. I had a goal, I had a dream and we achieved it.

“A lot of youngsters are coming up and winning grand slams. I think it’s great for women’s tennis. It is changing and has become more exciting for everyone.”

Kenin retained her beguiling innocence, a slightly overawed kid, still, in front of the world’s media late on Saturday evening, nursing a large glass of champagne and glancing over to her proud father for guidance. He is not an overbearing “tennis dad”, more a kindly mentor, who – like Maria Sharapova’s father before them – knew hardship and found a way out of it.

Kenin, who more than doubled her career earnings with a winner’s cheque for $A4.1m (£2.08m), stopped smiling long enough to reveal she would be raiding the Cartier shop in Melbourne . “I got my eye on a few things,” she said.

She has earned it.