Novak Djokovic celebrates during his third-round match against Kei Nishikori on Saturday at the U.S. Open in New York. Djokovic dropped the first set but rallied to win in four sets. John Minchillo/Associated Press

NEW YORK — Novak Djokovic did not seek to keep his thoughts to himself on court Saturday, the way he mostly did through his first two U.S. Open matches. Instead, he let it all out, slapping his chest or sneering with a fist raised to celebrate success, pointing to his ear to ask the crowd for noise.

This was the Djokovic everyone is so accustomed to seeing – yes, winning on the Grand Slam stage, of course, as he always does in this magical season, but also animated and into it, encouraging the spectators to join him for the ride on his path toward tennis history.

Taking another step in his bid to complete the first calendar-year Slam by a man in more than a half-century, Djokovic moved into the fourth round at Flushing Meadows for the 14th consecutive appearance, coming back to beat Kei Nishikori 6-7 (4), 6-3, 6-3, 6-2.

“I don’t plan to have those kind of emotional moments on the court, whether good or bad. It just happens,” Djokovic said. “In the heat of the battle, when you feel like the moment is very important … you just want to get those things out of yourself, out of your system – try to, I guess, ride on that energy wave that you create, whether it’s with yourself, whether it’s with the crowd.”

So the No. 1-seeded Djokovic managed to avoid the rash of upsets that have hit the tournament, but the top-seeded woman, Ash Barty, did not. A day after defending champion Naomi Osaka and two of the top five men, Stefanos Tsitsipas and Andrey Rublev, were beaten, Barty blew a big lead in the final set and lost to 43rd-ranked Shelby Rogers of the U.S. 6-2, 1-6, 7-6 (5) in a night match.

Rogers was a quarterfinalist in New York a year ago, while Barty owns titles from the French Open in 2019 and Wimbledon this July but never has been past the fourth round at Flushing Meadows.

Coming into this match, Barty was 5-0 against Rogers. She was up two breaks at 5-2 in the third set.

Rogers’ mindset at that point?

“Can’t get any worse. You’ve lost to her every time,” said Rogers, who plays 18-year-old Emma Raducanu of Britain on Monday. “Try something different.”

Djokovic, a 34-year-old from Serbia who is ranked No. 1, is now 24-0 in the sport’s four most important events this season, having won the Australian Open in February, the French Open in June and Wimbledon in July. The last man to go 4 for 4 at the majors was Rod Laver in 1969; Steffi Graf was the last woman, in 1988.

Win four more matches next week, and Djokovic also would earn his 21st career Slam trophy, breaking the men’s mark he currently shares with Roger Federer and Rafael Nadal.

It was in the fourth round last year that Djokovic’s U.S. Open ended; he was defaulted late in the first set for angrily swatting a ball that inadvertently hit a line judge in the throat. In 2019, an injury ended his trip to New York in the fourth round.

Now he’ll play wild-card entry Jenson Brooksby, who edged 21st-seeded Aslan Karatsev in five sets to become, at 20, the youngest American man in the round of 16 at the U.S. Open since Andy Roddick in 2002.

Other players advancing included Wimbledon runner-up Matteo Berrettini and No. 13 Jannik Sinner – they gave Italy a pair of men in the U.S. Open’s fourth round for the first time in the event’s 140-year history – along with Olympic women’s gold medalist Belinda Bencic, 2019 U.S. Open champion Bianca Andreescu, 2020 French Open champion Iga Swiatek and two-time major finalist Karolina Pliskova.

After eliminating a couple of inexperienced opponents ranked 121st and 145th, Djokovic faced someone with a far better resume in Nishikori, who was the runner-up at the 2014 U.S. Open and has been as high as No. 4.

Here, though, was the problem for Nishikori heading into this encounter: He’d lost his last 16 matches against Djokovic. And while Nishikori, to loud roars from the stands in Arthur Ashe Stadium, stole the first set, the march to No. 17 in a row was soon in progress.

“I don’t think I started off very well. I was quite passive. I was too far back in the court. He was dictating the play,” Djokovic said. “He played much quicker and more aggressive than my opponents in the opening rounds did.”

One key stat: Djokovic made 20 unforced errors in the first set, then reduced that to an average of 10 1/2 per set over the last three.

Here’s more: Djokovic came up with a high-for-him 15 aces and dropped serve a total of twice, while breaking Nishikori seven times.

And Djokovic reacted to vital moments with joy, eliciting similar displays from fans, who were barred from the tournament in 2020 because of the coronavirus pandemic.

When he broke to lead 2-1 in the second set by winning a fantastic point that ended with both men near the net, he spun around and yelled, mouth agape. In his guest box, his wife, Jelena, stood and shouted, “Come on!” When Djokovic saved a break point in the third set, he indicated he wanted louder cheers by reaching for his right ear, then wagging his fingers. When he broke to go up 5-3, he pursed his lips to say, “Ooh!” In the next game, he reacted to a netted drop shot by tapping himself on the head with his racket three times, then screamed when he took that set, first toward one side of the stands, then another.

Djokovic described his improved play as the match wore on, stretching past 3 1/2 hours, as “getting that groove back and getting that rhythm.”

In other words, he might just be hitting his stride heading into Week 2 on the hard courts.

He certainly looked comfortable in the moment Saturday.

“Maybe,” Nishikori said, “he’s feeling that inside – a lot of pressure – but I couldn’t see that during the match.”

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