Djokovic, also the top-ranked player in the world, beat Tallon Griekspoor of the Netherlands 6-2, 6-3, 6-2. The match lasted 1 hour, 39 minutes, a contrast to Djokovic’s first match, when he needed four sets to put away a qualifier.

Novak Djokovic, Alexander Zverev win easily at U.S. Open

Among areas of Djokovic’s dominance, he broke Griekspoor six times in 10 chances, while Griekspoor won one of four break points. Djokovic also dominated in aces (13-5) and winners (33-20).

“Great performance. Definitely better than the first-round match,” Djokovic said. “Obviously I’m very pleased with the way I came out on the court. I served very well, I found the rhythm on the serve. It was important that I came up with the goods.”

The win sets up a match with Japan’s Kei Nishikori, who needed just under four hours to defeat American Mackenzie McDonald 7-6 (3), 6-3, 6-7 (5), 2-6, 6-3. Nishikori has reached as high as fourth in the world rankings previously.

 “Obviously I love the challenge,” Nishikori said. “Now he’s one of the best on the tennis tour. It’s not someone I love to play all the time, because obviously he’s the toughest opponent, one or two. I’d rather have someone ranked lower. But I always love the challenge.”

No. 4 Alexander Zverev of Germany had an even easier time of it, losing only four games in downing Albert Ramos-Vinolas of Spain 6-1, 6-0, 6-3. The match lasted only 74 minutes.

At one point, Zverev won 13 straight games. He also kept up his roll of excellence on first-serve points, losing just eight total in his first two matches and not letting either of his opponents reach break point against him.

“My serve is kind of the key to my game,” Zverev said. “When it’s working, I’m playing great. When it’s not, I’m losing matches like I did at Wimbledon. … It’s no secret that my serve is probably the most important shot in my game, and I’m happy with how it’s working. … The matches are not going to get easier, and I will need that to be my weapon.”

Zverev’s next opponent will be American Jack Sock. The wild-card entry needed five sets and more than 3 1/2 hours to defeat Alexander Bublik of Kazakhstan, the 31st seed, 7-6 (3), 6-7 (2), 6-4, 4-6, 6-3.

Also losing was 10th-seeded Hubert Hurkacz of Poland, 2-6, 6-4, 6-4, 7-6 (6) to Italy’s Andreas Seppi, who is ranked 89th in the world.

Italy’s Matteo Berrettini, the sixth seed, needed four sets to turn back Corentin Moutet of France 7-6 (2), 4-6, 6-4, 6-3. Berrettini finished with 17 aces to four for Moutet, who is ranked 88th in the world. The battle lasted 3:21.

The 21st seed, Russia’s Aslan Karatsev, spotted Australia’s Jordan Thompson a two-set lead before roaring back for a 3-6, 3-6, 7-5, 7-6 (9), 6-1 win. Karatsev fought off two match points in the fourth-set tiebreaker.

Other seeded players to post wins were No. 13 Jannik Sinner of Italy, who needed four sets to knock off Zachary Svajda of the U.S.; No. 17 Gael Monfils of France, a four-set victor over American Steve Johnson, and No. 22 Reilly Opelka of the U.S., who defeated Lorenzo Musetti of Italy in three hard-fought sets.

In a match of Americans, wild-card entrant Jenson Brooksby knocked off Taylor Fritz 6-7 (7), 7-6 (10), 7-5, 6-2.

Seventh-seeded Denis Shapovalov of Canada was facing Spain’s Roberto Carballes Baena later Thursday.