The third-ranked Serb, who earned an ATP Tour-leading 67th win of the year, got match point with his 10th ace and won when Beck netted a forehand.
"My strokes were very solid today. I could have finished the match in a shorter time but he pulled out some good serves," he said.
Djokovic is playing in the main draw for the first time and could meet hometown favorite Roger Federer in the final. He said he had received "great hospitality" at Federer's home event. Federer faces Italy's Andreas Seppi in the second round on Wednesday.
"It's normal that everyone is looking at him," Djokovic said. "Bottom line is that he's the best in the world."
Djokovic next plays 59th-ranked Jan Hernych of Czech Republic, who beat Australia's Peter Luczak 6-3, 6-4.
Djokovic twice broke Beck's serve for a 5-1 lead, but dropped serve and then wasted a set point at 5-2.
He replied with a service game at love, clinching the set with a drop volley that balanced on the net cord before falling forward.
The second set went with serve through 10 games, though Djokovic had to rally from 15-40 when trailing 4-3.
Djokovic created his break opportunity with a double-fisted backhand passing shot, then took it when Beck sent a forehand long.
Chiudinelli, was soon back on court partnering childhood friend Federer in the doubles. The two local residents lost 6-4, 6-3 to James Cerretani of the United States and Aisam-Ul-Haq Qureshi from Pakistan.
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