Naomi Osaka returned to the Flushing Meadows taking advantage of some early jitters for Anett Kontaveit and showing no ill effects from a recent left hamstring problem.
The fourth-seeded Osaka never faced a break point and beat the 14th-seeded Kontaveit 6-3, 6-4 in Arthur Ashe Stadium.
Osaka owns two Grand Slam titles, including Flushing Meadows in 2018. She lost in the fourth round a year ago.
Kontaveit won the match's first point, but followed that with a pair of double-faults, followed by a pair of backhand errors to get broken.
And Osaka was on her way, winning 35 of 45 service points.
Djokovic's departure means there is no man left in the field who has won a Grand Slam singles title. Whoever emerges as champion will be the first first-time major trophy winner in men's tennis since 2014, when Marin Cilic won the US Open.
Plus, each of the last 13 Grand Slam trophies had been won by a member of the Big Three of Federer, Nadal and Djokovic.
World No.93 Shelby Rogers continued her stellar campaign as she defeated No.6 seed Petra Kvitova to enter the last eight in the women's singles event.
On Sunday, US' Rogers saved four match points as she beat Kvitova 7-6(5), 3-6, 7-6(6) to make it to the quarter-finals at her home Grand Slam event for the first time at the Flushing Meadows.
"Day 72 in the bubble," Rogers joked to laughter from the media during her post-match press conference as per the WTA website. "It's been a long time here in New York. I'm happy to be sticking around for some more."
"The tiebreaker, the whole match actually, was a little bit of a roller coaster for both of us," said Rogers. "The first set, you know, a tiebreak. (Kvitova) upped her level a little bit in the second there. I was up a break in the third, she breaks back. She's just hitting missiles. She served unbelievable.
"To get that double-fault there in the (third-set) breaker, a little luck was on my side today I think. I just kept trying to hang in there and defend her balls, take care of my serve there in the third after I got broken. Thankfully somehow got it done," she added.
Rogers will next square off against either 2018 champion Naomi Osaka of Japan or 14th-seeded Anett Kontaveit of Estonia.
Grand Slam champion, (that's) all I know. No Grand Slam champions left in the draw. Now it gets interesting," said Zverev, who beat Alejandro Davidovich Fokina 6-2, 6-2, 6-1. "Now I think is the time when it gets really interesting."