Coco Gauff, at age 15 and in her first United States Open singles tournament, got it just right.

What makes Naomi Osaka special is her capacity to lock in and play ruthless tennis, and then, with the handshake complete, to zoom out and have the humanity to sense the bigger picture.

It is a rare and appealing combination. And it was on full display in Arthur Ashe Stadium on Saturday night as Osaka, the world No. 1, played one of her finest and most focused matches to overwhelm Gauff, the sport’s latest prodigy, 6-3, 6-0. Osaka, only 21 herself, then immediately put herself in her crestfallen young opponent’s sneakers, helping her turn a negative into a positive.

“For me, the definition of an athlete is someone who on the court treats you like your worst enemy but off the court can be your best friend,” Gauff said later. “I think that’s what she did tonight.”

As tennis epigrams go, Gauff’s definition of an athlete might deserve a spot alongside “pressure is a privilege,” or “if you can meet with Triumph and Disaster and treat those two impostors just the same.”