Djokovic, whose winning streak stretches back to October and includes claiming a third straight Australian Open title, was broken once in the second set but was otherwise untroubled in his first match since Davis Cup duty earlier this month.
"I had three or four weeks of no tennis, so I was extremely focused to start well and I did really well in the first set," the 25-year-old said.
"I was right behind his serve and I'm very satisfied with my performance and hopefully I can continue."
Also into the second round is former US Open champion Juan Martin Del Potro, who saved three match points on his way to beating Marcos Baghdatis 4-6, 6-4, 7-6.
"Marcos also deserved to win but the luck was behind me and I played better in the big moments," Del Potro said.