The Australian Open champion broke Ljubicic at love in the eighth game of the first set for a 5-3 lead and clinched the set with an ace.
Using a two-handed backhand to counter Ljubicic's booming serve, Djokovic saved two break points in the eighth game of the second set but was rarely troubled.
"I came up with a straight-set win, which is very important for me at the start of the clay-court season," Djokovic said. "I played my best tennis in the most important moments, and that's what actually matters most."
After missing the chance to even the score at 4-4, Ljubicic's serve withered in the next game and Djokovic won on his first match point when Ljubicic hit a forehand into the net from the back of the court.
Djokovic said he took more time than usual to find his rhythm before pulling away.
"That's why I got off to a nervous start," Djokovic said. "But then I played at a very good level."
Djokovic's best showing on clay so far was last year's title at Estoril, Portugal.
"One of the things that I really try to have this year is patience," Djokovic said. "On the other hand, I'll try to be myself and be aggressive, the kind of style of game that I always have. So it's going to be a real test for me."
"I don't want to push myself too much and focus on the points and rankings," Djokovic said. "I know I have enough potential to be top of the world. But I'm only 20 years old, I still have a lot of time ahead of me."
Neither player looked comfortable in an error-strewn match, but the 12th-seeded Robredo capitalized on more opportunities and broke Wawrinka's serve six times. He faces Robin Soderling of Sweden in the second round of the clay-court tournament.