The Serb, who was also pushed to four sets in punishing daytime temperatures above 90 Fahrenheit (32C)in the first round, was far more comfortable in the evening at the Arthur Ashe Stadium, breaking early and running away with the opening set in 31 minutes.
The 31-year-old was two sets up and leading by a break in the third when he spurned a match point, allowing Sandgren to force a tiebreak that the American won easily.
Djokovic, however, recovered well, achieved an early break in the fourth set and closed out the match in two hours, 45 minutes.
"I thought I played really well in the first two sets and then I lost it mentally," Djokovic said courtside. "I lost my composure and concentration but I got it back in the fourth."
The sixth-seeded Serb, who won Wimbledon this year, will face 26th seed Richard Gasquet of France in the third round.
(Reporting by Simon Jennings; Editing by Greg Stutchbury)
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