Djokovic advanced to the Round of 16 for the 10 consecutive year when Russia's Mikhail Youzhny retired after just six games Friday in their third-round match at Flushing, N.Y.
The 31-minute victory sent the defending champion into a matchup against either American John Isner or Great Britain's Kyle Edmund.
The top-seeded Djokovic won his opening match in four sets before moving on with a walkover in the second round.
Djokovic won the first three games against Youzhny, who informed the umpire he was done after delivering a forehand winner to close out the sixth game.
Ninth-seeded Jo-Wilfried Tsonga of France also advanced to the fourth round by dispatching Kevin Anderson of South Africa in straight sets, 6-3, 6-4, 7-6 (4).
It is the fifth consecutive year Tsonga is in the Round of 16, setting up a match against American Jack Sock, who stunned No. 7 seed Marin Cilic with a 6-4, 6-3, 6-3 victory.
Sock converted four of six break points against the big-serving Cilic and needed only 1 hour, 41 minutes to complete the upset of the 2014 U.S. Open champion.
Also moving on was 10th-seeded Frenchman Gaels Monfils, who breezed to a 6-4, 6-2, 6-4 win over Nicolas Almagro of Spain.
Up next for Monfils is Cyprus' Marcos Baghdatis, who advanced to the fourth round at a major for the first time since 2009 by beating American Ryan Harrison, 6-3, 7-6 (4), 1-6, 6-1.