“I felt like I shouldn’t let myself be overcome by nerves or anything,” Osaka said. “And I should just really focus on playing tennis because that’s what’s gotten me to this point.”

That is easily said but rarely achieved, and though Osaka was the portrait of poise and focus on Saturday, that has not been the case throughout her short career. She has struggled with negativity, self doubt, shot selection under pressure and consistency.

Only two years ago, she blew a 5-1 lead in the third set to lose to Madison Keys in the third round of the U.S. Open as her movement and nerves betrayed her. And though she was brilliant in winning the title at the BNP Paribas Open in Indian Wells, Calif., in March this year, she lost in the first round in her two lead-in tournaments before this U.S. Open.

But with her new coach Sascha Bajin setting a positive tone, she became a champion in New York.

“Ultimately, you never know what you’re made out of until you’re tested,” Bajin said. “Naomi was thrown in there into deep water today. Got everything thrown at her: big bombs by Serena, the crowd, the drama. She remained with her composure. There are certain things you can train yourself to do; other things you just have, and I believe it’s a gift, what Naomi has.”

She arrived with no nagging injuries and her improved fitness allowed her to stay in rallies longer without feeling the need to go for broke. Her footwork, particularly the quick adjustment steps, is also much improved, and her leg drive has increased her serving power and her ability to hit flat, full-force serves to all sections of the box.

But many players have improved their fitness and technique on tour. So few could have managed an occasion like Saturday with this kind of aplomb. The final was remarkably intense from the opening point, an extended, big-hitting baseline duel won by Osaka.