The timing couldn't be better for Djokovic, who has struggled with his own arm and wrist injuries since the Rio Olympics. In his first-round match on Monday, a four-set struggle against Jerzy Janowicz, Djokovic called for the trainer only five games into the match to work on his arm.
Afterward, Djokovic didn't want to go into details, saying in his on-court interview, "I don't think it's necessary to talk about this now. I'm through. I'm taking it day by day."
But before the tournament began, the world No. 1 said his wrist had not been "ideal for the last 3½ weeks."
Djokovic has been mired in a rare slump. Since winning the French Open in early June, he lost to Sam Querrey in the third round of Wimbledon. He did rebound in Toronto, capturing the Rogers Cup trophy, but his success was short-lived.
In Rio, the Serb, who has won six of the past nine Grand Slam events, was stunned by Juan Martin del Potro in the opening round.
A title at the US Open, however, would make Djokovic only the second player in the Open era -- joining Roger Federer -- to win three Slams in consecutive seasons.
Nadal's victory came after the new, $150 million roof in Arthur Ashe Stadium was closed with the score 3-3 in the second set.
American John Isner beat Steve Darcis -- who was also coming off a five-set match -- 6-3, 6-4, 6-7 (10), 6-3 in 2 hours, 54 minutes to reach the third round. Both rallied from two sets down in the first round: Isner spent 3 hours, 27 minutes on court on Monday, while Darcis needed 4 hours, 11 minutes.
The 20th-seeded Isner had a chance to close out the victory against Darcis in the third-set tiebreaker but wasted four match points.
The 106th-ranked Darcis also faced the extra fatigue of going through qualifying to make the main draw.
Isner improved to 9-0 in US Open second-round matches. He had 38 aces on Wednesday, when he received treatment on his right knee and for blisters on his foot.
Marin Cilic, the 2014 US Open champ, also advanced.
The seventh-seeded Cilic needed just 1 hour, 40 minutes to beat Sergiy Stakhovsky 6-1, 6-2, 6-3.
The fifth-seeded Raonic was treated by a trainer for problems with his left wrist and left thigh during Wednesday's match and generally looked weary as play went on.
Information from The Associated Press was used in this report.