The third-seeded German was joined in the second round by sixth-seeded Viktor Troicki of Serbia, who battled past Bjorn Phau of Germany 6-3, 3-6, 6-4.
Injury-plagued Russian Nikolay Davydenko, whose ranking has fallen to No. 48 from a high of No. 3, cruised past Victor Hanescu of Romania 6-2, 6-3.
Kohlschreiber outlasted his opponent with a gritty display. With both players holding serve throughout the first set, Kohlschreiber finally found a forehand winner in the tiebreaker.
"It was a good first set and he never gave me any easy balls," said Kohlschreiber,
After breaking Dodig in just the second game of the second set, the German pressed his advantage and broke again in the fourth before wrapping up the match.
Troicki was stretched hard in a thrilling match that lasted 1 hour, 45 minutes.
"I knew it was going to be a tough match, especially since it was the start of the season. Bjorn played really well and it was a tight match indeed. I'm happy to finish my match before the New Year started," said Troicki, who had seven aces.
Top-seeded David Ferrer and second-seeded Richard Gasquet of France play their opening-round matches
The $1.05 million tournament is missing many of the game's biggest stars with Ferrer and Gasquet the only top-10 players taking part.


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