The 33-year-old striker, who came on after the interval, latched onto a through pass from teammate Wu Xi before sending it into the net in the 65th minute.
Djokovic will face Jan-Lennard Struff for a spot in the round of 16. The German needed one hour and 40 minutes to move past American Michael Mmoh 6-2, 6-2, 7-5.
"Kyle played a fantastic first set," added Djokovic. "He didn't do much wrong, he served very well and was aggressive from the back of the court. Usually his forehand is a weapon, but his backhand, especially in the first set, was very strong, very solid."
Rondon continued to demonstrate his prowess in the second half. In the 48th minute, the Venezuelan striker assisted Swedish winger Sam Larsson to stretch the lead for Dalian.
Garcia looked untouchable in the first set and for much of the second, blasting 30 winners and breaking Pliskova's serve three times en route to the 6-1, 7-6 (2) victory.
"There have been other instances where we have tried to go but the club won't allow it, or they've done something. I want to play football, I am still motivated to play football, so I guess it's on the club. They are in control of everything. I have a contract, all I can do is carry on what I am doing and hopefully something comes up," said Bale. Enditem
The 54-year-old Dane announced he has been receiving medical treatment for the condition after being diagnosed some years ago and, with the assistance of doctors, has continued to carry out his duties as BWF president "without limitation," said the world governing body.
"I was really focused each game and each point. Especially against top players, one point can make the difference. So I had to stay very calm and keep going," the world number 50 added.
The 23-year-old Dutchman has signed a five-year contract at Old Trafford, with an option to extend by a further year. The transfer fee is 39 million euros (46 million U.S. dollars), which may increase to 44 million euros if certain clauses are met.
He doubled Flamengo's lead with a low shot that rebounded in off the post before Rodriguinho pegged a goal back for the hosts.
"It was anybody's game really for a set and a half. I made some breaks and then obviously after winning the second set I felt more comfortable. I was returning better, I started to read his serve better, and I was pleased with my serve. Overall, it was a very good test, and I am happy to get through," said Djokovic, who is bidding to capture his fourth US Open trophy and 18th Grand Slam title.