Djokovic was broken in the ninth game of the first set to fall behind 4-5, but broke right back and forced a tie-breaker, which he won 7-2 before cruising the rest of the way.
The 26-year-old Serb said he had trouble with his footwork in the tricky conditions against a dangerous opponent in 87th-ranked Becker, best known for beating Andre Agassi at the 2006 US Open in the last match of the American's career.
"It was a struggle," Djokovic, the 2011 US Open winner, said about the opening set.
"I tried to move him around the court...that was my tactics.
"But it was very tough. It was a lot of unforced errors, very windy conditions."
Djokovic made an uncharacteristic 18 unforced errors in the first set before getting comfortable with his approach on the blustery court - an adjustment that might pay dividends as the tournament progresses.
"It was a lot of wind, wind that is not consistent. It changes direction all the time, you have to be alert," added Djokovic, stressing the importance of being balanced when attacking the ball.
"You need to have this adjustment, footwork, steps, in order to get on the ball. I didn't have that in the first set."
Djokovic adapted and after the 52-minute first set struggle won the next two sets in a total of 59 minutes.
"After I played a good tiebreak, then everything kind of settled. I started to serve better," said Djokovic, who belted in 13 aces.
"I started to step into the court, which is important." Djokovic, who lost in five sets to Andy Murray in last year's final in Flushing Meadows, has designs on adding to his haul of six Grand Slam titles.
"My game is getting there. I feel that it was a big test for me today. It was a challenge and I needed to overcome it."
Djokovic will next face either Finland's Jarkko Nieminen or Portugal's Joao Sousa.
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