NEW YORK -- Roger Federer gave one of his regularly scheduled master classes in tennis to an ambitious understudy in the bright sunshine before a near capacity crowd in Arthur Ashe Stadium on Saturday afternoon. But this time the sliced backhands and pinpoint serves were the least of it.

The underlying theme on this occasion was Federer's professionalism, and by the time he put the finishing touches on his tidy 6-4, 6-1, 7-5 third-round win over Nick Kyrgios, the Aussie was moved to pay tribute to the 37-year-old paragon.

"I think we're two very different characters," said Kyrgios, who's on-court antics tend to generate controversy. "I think, just the way he goes about things. I could take a leaf out of his book. The way he behaves on court, you know, his demeanor. I don't want to change myself too much, but I could definitely take away things he does in certain situations. He's the ultimate role model to anyone who wants to play."

It was a strange, but also gratifying, tribute coming from Kyrgios. After all, he had no reservations about mimicking Federer's service action during play in the first set -- a gesture that might have incensed a less imperturbable rival.

Not Federer. "Sure, it's unusual to happen against you, with your own serve." Federer said. "He was in a mood to be gracious, and given the score line, he could afford to it. He's been using my serve sometimes to great effect, which I'm very happy to see. No, I'm joking. Look, I take it like just as it is."

That was a signature incident, demonstrating Kyrgios' showmanship and nerve -- not to mention the talent that allows him to even conceive such a stunt. That he does such things in the heat of a significant tennis match is impressive in the same way as a forest ranger putting his head inside the mouth of a grizzly bear. It's fun to watch, but few forest rangers try it.

Kyrgios came into this match 1-2 against Federer, with every one of those matches having gone to a third-set tiebreaker. There's no denying Kyrgios' genius: He's quicker than a cat, full of tensile power; his game goes off like a bottle rocket overloaded with gunpowder. But he falls into foul moods, loses inspiration and makes terrible choices. At such times, he's the anti-Federer.

Early in the match, it appeared this might be another close, tension-fraught meeting between icon and iconoclast. The men ripped through the first six games on serve, but Federer stumbled and fell behind 0-40 in the seventh game. He was serving badly. His backhand was all over the place. Kyrgios was playing, to use Federer's word, "inspired."

"I knew it's just huge to try to get out of it [that game] somehow," Federer said. "Doesn't have to be pretty. Doesn't have to be crazy shot-making. Just you have to get back to deuce somehow and maybe you can breathe a bit."

Roger Federer improved to 53-1 in the first week of the US Open in his career. Robert Deutsch/USA TODAY Sports

Federer executed that survival plan, one that led to Kyrgios muffing a few easy backhand service returns. It was a lesson in enduring adversity, but Kyrgios wasn't really paying attention. The pressure mounted on his hit-and-miss game. When Federer converted set point with Kyrgios serving at 4-5, the Aussie turned and began berating his support team in the player box.

"Pressure," Kyrgios said, rationalizing the outburst. "You know, got to the business end of the first set, crucial moment. Played a terrible service game. I knew how important that first set was. He loosened up straight away after that. He started playing some shots that we all know he can make. When he gets in front, there's not much you can do."

It was a fair assessment, yet it doesn't really pay adequate homage to the Federer ideal. Kyrgios, too, is a spectacular shot-maker. The difference is he will often choose to go for the spectacular shot, when a safer, effective one would do, while Federer's shot selection is almost always unimpeachable. That willingness to pull the trigger on an unexpected shot is Kyrgios' trademark, but it has a heavy price tag.

"Other guys play the shot you're supposed to hit, and then if you get beat, you're, like, 'Maybe I should have hit Nick's shot,'" Federer said. "Nick goes the other way around. He hits that shot, but then if he doesn't win that point, maybe he tells himself, 'Well, maybe I should have hit a normal shot.'"

play 1:10 Federer's victory over Kyrgios full of highlight-reel moments Roger Federer impresses in his match against Nick Kyrgios, but his running forehand winner may be the shot of the tournament as captured on the AI IBM Highlights.

Federer provided a vivid illustration of his point. Serving at 5-all, 40-15 in the third set, Kyrgios attempted a surprise drop shot at the wrong moment. Had he made the shot, Federer would have found himself challenged to hold serve to get into a tiebreaker. Instead, the drop shot never cleared the net, and Federer went on to break serve.

"He chooses to go for sort of the drop shot, which at the end cost him the match," Federer said. "That's why we go back to being super consistent, make him hit that one extra ball, because when you play like this, it can also work against you."

Federer's unique talent is to play spontaneous, free-flowing tennis that never betrays an underlying, severe discipline. It isn't just that his shot selection is impeccable; he also patiently endures the wild fluctuations, antics and distractions created by a player like Kyrgios. If any of this can rub off by osmosis, Kyrgios might have learned something Saturday. It might be the only way he would, as he has resisted hiring a full-time coach. He's no more certain of what lies in his future than anyone else.

"I get told a lot, 'What do you want from your career?'" Kyrgios said. "I wouldn't say I'm satisfied with my career. I think there is a lot more to be done. ... I have been around for about four years now. I have barely done anything. I think I can do a lot more. As I said, it's all mental with me, I think. If I want it enough, I have a coaching option, psychology option. I think there is a lot more things to explore."

They say even the longest journey begins with a first step. Perhaps the lesson inflicted on Kyrgios on Saturday will be that step.