“I did enjoy it, but I also suffered a lot on the court,” Djokovic said.
“It was a very close match. He was probably the better player for the first set and he didn’t give me time to breathe.
“I think I dug myself out of trouble with good serving, which obviously makes me happy.”
Djokovic will face big-serving German qualifier Yannick Hanfmann in the third round.
Sixth seed Ben Shelton looked rusty as he lost 6-2 6-4 to David Goffin of Belgium.
The 22-year-old American, who has been recovering from a shoulder injury picked up at the US Open, struggled to find his rhythm in the first set and lost his serve in the third and seventh games.
Shelton battled back in the second but an unforced error in the ninth game handed Goffin the advantage and the world number 83 closed out the contest.
Goffin’s reward is a third-round match against Canada’s Gabriel Diallo, who is seeded 31.
World number one Carlos Alcaraz pulled out of the Shanghai Open earlier this week with the Spaniard citing “some physical issues” after winning the Japan Open.
