Second-seeded Djokovic trailed 4-0 in the opener before recovering to 5-5 and finally finding his form in the tiebreaker, where his 63rd-ranked German opponent won only one point.
The second-ranked Serb broke serve in the first and last games of the second set to close out the match.
Djokovic next plays either Horacio Zeballos or Florian Mayer in the second round.
Top-seeded Andy Murray plays 69th-ranked Jeremy Chardy of France in his opener on Tuesday.
Murray, who took the top ranking from Djokovic at the end of last year, was in action on Monday with Mariusz Fyrstenberg in the doubles. The pair lost to David Marrero and Nenad Zimonjic 6-2, 6-4.
Original author: AP