The Serbian will play either Florian Mayer of Germany or Argentine Horacio Zeballos in the second round.
"It's the first match of the year. You never know how you're going to start," Djokovic was quoted as saying on the ATP's website (www.atpworldtour.com).
"I was a bit flat on my feet. But I stayed composed because I knew, I believed that I could find the rhythm, start reading his serve better, and that's what happened.
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"I know that I can't be at my top the very first match, but I believe that the process is right."
Murray, who lost a first-round doubles match with Mariusz Fyrstenberg on Monday, plays Frenchman Jeremy Chardy on Tuesday.
The Scot won the title in 2008 and 2009.
(Reporting by Martyn Herman in London; Editing by Clare Fallon)
