Djokovic — who has won three of his men’s record 23 Grand Slam titles at Flushing Meadows — needed to come back from a two-set deficit in the third round before eventually winning in five against Laslo Djere.
This time, Djokovic played far more cleanly and was in control throughout. He finished with only 12 unforced errors, while Gojo made 40.
“Just glad to get through in straight sets,” said the second-seeded Djokovic, who already is assured of replacing Carlos Alcaraz at No. 1 in the ATP rankings next week.
Djokovic won five of the big-serving Gojo’s 15 service games while only getting broken once himself.
Next up for Djokovic will be a matchup against No. 9 seed Taylor Fritz, a 25-year-old from California, who is the only remaining player in the men’s bracket to not have dropped a set so far.
Djokovic owns a 7-0 head-to-head career record against Fritz.
“I’m not going to talk about what he needs to do to have a chance against me. I’m sure he’s going to try to figure that out with his coach,” Djokovic said. “I’m going to get ready, obviously, for that match as any other match, doing my analytics, watching the last match we had against each other.”
Their matchup on Tuesday will be Djokovic’s 13th quarterfinal in New York and Fritz’s first.
“I need to play within myself and trust that if I’m playing well, then that’s going to be enough, and I don’t need to kind of do anything extra,” said Fritz, who defeated Swiss qualifier Dominic Stricker 7-6 (2), 6-4, 6-4 earlier Sunday.
Fritz is one of three American men who won fourth-round matches, along with No. 10 Frances Tiafoe and unseeded Ben Shelton. It is the first time a trio of men from the United States made it to the quarterfinals at Flushing Meadows since 2005, when Andre Agassi, James Blake and Robby Ginepri did it.
“That’s amazing, obviously, for the (U.S. Tennis Association), for the U.S. Open, as well,” Djokovic said. “All of the guys — Fritz, Shelton and Tiafoe — (use a) big serve, just very aggressive play.”