When Ajla Tomljanovic was a little girl, she asked her father about a prized photograph of him holding a big trophy on his head. Ratko Tomljanovic was a great professional handball player, winning two European Championships for Zagreb, the capital of Croatia, and was the captain of the Croatian national team; before that, he was a member of the Yugoslavian team.

But on Friday night, Tomljanovic, who is ranked 46th, demonstrated to herself and the world that she had the mettle and the shotmaking ability to win a trophy of her own. If she wins four more matches in the coming week, it will be one of the most coveted in sports.

That night, Tomljanovic beat the six-time U.S. Open champion Serena Williams, 7-5, 6-7 (4), 6-1, in front of a raucous, partisan crowd in Arthur Ashe Stadium in New York to advance to the fourth round of the U.S. Open for the first time.

“I feel like I belong here now,” she said.

That was not necessarily what she was thinking in the moments before she took the court.

Tomljanovic was nervous, and for good reason. Williams was her idol, and Tomljanovic had never played her before. She had never played in Ashe. In fact, she had never even practiced on that court. She had asked tournament organizers if they could find a time for her to hit some balls in the largest tennis stadium in the world at least once, but nothing was available.

Then there was the matter of her playing the role of villain, of facing down nearly 24,000 fans, virtually all of them screaming for Williams to win, and millions more watching on television. It would make anyone a tad nervous.

Tomljanovic confided the anxiety to her father, who was happy that his daughter admitted to the nerves. Better than hiding them, he thought. Ratko Tomljanovic also knew about playing in hostile environments, especially in Europe, where handball is intensely popular and the stakes are high. He tried to calm Ajla by evoking the almost comical role of the hard-bitten veteran of scrappy handball matches — the kind of yarn he had spun to her and his other daughter, Hana, many times before.

“Don’t tell me you are afraid of the crowd,” he told Ajla. “I played in some terrible places with 5,000 people booing and spitting, and one time the crowd came on the floor and there was a big fight. Don’t tell me it’s hard because some guy in the 35th row is yelling at you.”

It was not exactly Mickey yelling at Rocky. It was a speech designed to lighten the mood, and it worked. Ajla laughed. “She doesn’t care about what I did, at all,” Ratko said, chuckling.

But then he brought out another motivational tool. He mentioned one of his favorite movies, “For Love of the Game,” in which a pitcher for the Detroit Tigers, played by Kevin Costner, reflects on his life and career in the midst of a perfect game.

“But she didn’t know the movie, so I had to explain it to her,” he said. “I told her, ‘You have to be Kevin Costner today.’”

In the film, he told her, the pitcher focuses explicitly on the catcher’s glove and ignores everything else in the stadium. Ajla understood, and she followed the advice with her own unique resolve.

She blocked out all the noise, the roars for Williams, the indecorous cheers when Tomljanovic missed a serve, all the celebrities in the stands, the video tributes to Williams and her own childhood adulation for Williams, a 23-time Grand Slam champion standing across the net and playing as well as she had in years. But Tomljanovic was better.

“From the first moment I walked on court, I didn’t really look around much,” she said. “I was completely in my own little bubble.”

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