Like Djokovic, last year’s runner-up Taylor Fritz also dropped the first set but came through 4-6 7-6 (7-3) 6-2 6-4 against South Africa’s Lloyd Harris.
Fourth seed Fritz, the highest-ranked American in the men’s singles draw, will now face Jerome Kym after the Swiss qualifier upset 30th seed Brandon Nakashima of the United States.
Fritz was joined in round three by two-time semi-finalist and 17th seed Frances Tiafoe, who beat fellow American Martin Damm 6-4 7-5 6-7 (8-10) 7-5.
Twelfth seed Casper Ruud became the second-highest men’s seed to fall so far, losing 6-4 3-6 3-6 6-4 7-5 to Belgium’s world number 107 Raphael Collignon.
It completes a miserable year of Grand Slam results for Norwegian Ruud, who also lost in the second round of the Australian and French Open, and missed Wimbledon with a knee injury.
Collignon now meets 20th seed Jiri Lehecka, who progressed with a 3-6 6-0 6-2 6-4 win over Argentina’s Tomas Martin Etcheverry.
Another seed to fall was 16th-ranked Jakob Mensik – the 19-year-old, who is the highest-placed teenager in the world rankings, lost 7-6 (7-2) 6-7 (5-7) 6-3 4-6 7-6 (10-7) to Ugo Blanchet of France in a match lasting almost four-and-a-half hours.
It was a good day for other Frenchmen at Flushing Meadows, too, as Arthur Rinderknech upset 18th seed Alejandro Davidovic Fokina 6-4 3-6 2-6 6-2 6-3 in a five-set tussle, to earn a third-round meeting with compatriot Benjamin Bonzi.
Bonzi, who knocked out Daniil Medvedev in an extraordinary first-round marathon, went the distance again, coming from two sets down to beat Marcos Giron of the USA.
Meanwhile, 21st seed Tomas Machac of the Czech Republic saw off rising Brazilian star Joao Fonseca in 7-6 (7-4) 6-2 6-3.