The world number one cruised to a straight-sets victory in the Serbian's second-round tie against Giraldo.
"I am trying to be physically fit and fresh for the upcoming rounds," said Djokovic. "The longer the tournament goes, the tougher it gets. Especially in the opening rounds you are trying to get the rhythm to play well in every match.
"You can't underestimate any opponent and Santiago is a tricky player. It was really important to win the first set."
The 24-year-old will face Frenchman Nicolas Mahut in the third round of the tournament in Melbourne.