Rafael Nadal survived an epic 28-minute tiebreak to seal his spot in the quarter-finals and top seed Ashleigh Barty joined him with victory over giant-killer Amanda Anisimova on Sunday.
Nadal contracted Covid last month and said he was a big believer in getting vaccinated to stem a pandemic in which "a lot of people had been dying".
Gritty big-serving Italian battled back to win a second set tie-break before the Russian got a crucial break in game three of the third set to carve out a 6-2, 6-7 (5-7), 6-4 win.
German world number three Zverev came through a workmanlike 6-4, 6-4 clash against American Taylor Fritz, his second straight win of the new season.
ATP Finals 2021: Daniil Medvedev edges Alexander Zverev in thriller, Jannik Sinner beats Hubert Hurkacz
Sinner replaced fellow home hope Matteo Berrettini in the draw who pulled out due to abdominal injury.
Defending champion Daniil Medvedev triumphed 6-7 (5/7), 6-3, 6-4 over seventh seeded Hurkacz.
Medvedev says this comprehension of just how great a player Djokovic is will not reach full bloom quickly.
Andrey Rublev, Casper Ruud and Matteo Berrettini won their singles matches as Team Europe jumped to a 3-1 lead over Team World following the opening day of the fourth edition of the annual tennis showdown.
US Open 2021: Novak Djokovic tops Berrettini in quarter-finals with comeback win, will face Zeverev next
Djokovic ceded the opening set for the third consecutive match at Flushing Meadows but he quickly corrected his strokes and beat Berrettini 5-7, 6-2, 6-2, 6-3.
Zverev, last year's US Open runner-up to now-injured Dominic Thiem, reached his fourth career Slam semi-final and could find himself matched against history-chasing Djokovic on Friday.
Djokovic beat Berrettini in the quarterfinals of the French Open in June, then came back after dropping the first set to top the Italian again at the All England Club in July.
World number one Djokovic rallied past 99th-ranked Brooksby 1-6, 6-3, 6-2, 6-2 to book a quarter-final encounter with Italian sixth seed Matteo Berrettini in a rematch of July's Wimbledon final.
US Open 2021: Novak Djokovic launches calendar Slam quest with win; qualifier stuns Pablo Carreno Busta
Fourth-seeded Zverev, coming off Japan gold and a title two weeks ago at Cincinnati, dispatched American Sam Querrey 6-4, 7-5, 6-2 in a first-round match at Arthur Ashe Stadium.
US Open 2021: Novak Djokovic motivated by 'unique opportunity' as challengers look to thwart attempt at history
Only two men have won all four majors in a calendar year. Don Budge was first in 1938 and legendary Rod Laver managed the feat twice – in 1962 and 1969. In the 52 years since, no man had won the first three Slams of the year until Djokovic has in 2021.
US Open 2021: Novak Djokovic faces potential Wimbledon final rematch against Matteo Berrettini in quarter-finals
Under a men's singles draw released Thursday by the US Tennis Association, the 34-year-old Serbian top seed was placed in a draw quarter that could see him meet Australian fourth seed Alex de Minaur in the fourth round.
Halep only returned to the Tour last week in Montreal, losing in the opening round. She remained confident that progress was not far away after her injury in Rome three months ago.
World number eight Berrettini picked up the injury in London where he became the first Italian to reach a Wimbledon singles final, losing in four sets to Novak Djokovic.
Even at 19 Grand Slams, Novak Djokovic had a strong case to be over-and-above Roger Federer, Rafael Nadal in GOAT race. With 20th, at Wimbledon, he has removed all doubts.
Super Sunday: Messi's dream fulfilled, Djokovic joins '20' club, Italy inflict pain on England to clinch Euro title and more
Check out photos from the Super Sunday blockbuster in sports, as Lionel Messi ended his long wait, while Italy broke England hearts in Euro 2020 final at Wembley.
In Numbers: Novak Djokovic wins Wimbledon, goes level with Roger Federer, Rafael Nadal on 20 Grand Slam titles
With his sixth Wimbledon title, Novak Djokovic equalled the record for most Grand Slams among men with his storied rivals Roger Federer and Rafael Nadal.