The 24-year-old Serb, who used last year's Australian Open to catapult him to the world's top ranking and three Grand Slam titles, took a little time to get going in the warm Melbourne sun before he moved through the gears.
Djokovic moved the Colombian around the court with ease, mixed up his pace and angles with several audacious drop shots before the world number one came through in one hour, 42 minutes when Giraldo's backhand sailed long.
Djokovoic will meet Nicolas Mahut in the third round, after the Frenchman came back from a set down to beat Tatsuma Ito of Japan 1-6 7-6(6) 6-2 6-2.
Djokovic makes his acting bow in the blockbuster "The Expendables 2" later this year but the defending champion showed that he had lost none of his appetite for his day job with an emphatic second round victory at Melbourne Park.
Djokovic revealed after his match that he gets into a fight in his movie debut and, if the first film in the series is anything to go by, it is likely to be more of a dramatic tussle than the crowd on Rod Laver Arena witnessed on Thursday.
"A win is a win however it comes to you. I try obviously to not underestimate any opponents in early rounds," the Serbian told reporters afterwards.
"Santiago came out early hitting the ball quite flat but I knew that sooner or later he's going to drop the rhythm and I just have to hang in there. I've done a good job."
There was a brief blip in the first set, when four unforced errors handed Giraldo a service break, but the world number one broke back to love immediately and said there had been no nerves.
"To be honest, I've had lots of situations where I was break down in my career so I guess that doesn't affect me, especially early in the first set," he said. "I knew that I would start hitting the ball better."
Andy Roddick's 11th Australian Open campaign ended in disappointment when he was forced to retire against Australian Lleyton Hewitt when trailing two sets to one.
He draped his towel over this right shoulder, limped across to umpire Enric Molina, shook his hand, picked up his bag and disappeared down the tunnel at Rod Laver Arena, a 3-6 6-3 6-4 loser.
The pair were expected to bash each other across the Melbourne Park centre court until the small hours on Friday.
Instead, an awkward off-balance lunge by Roddick early in the second set when he slowly rolled over on his right ankle effectively ended the contest.
The 2003 US Open champion appeared dejected at the end of the game and called for the trainer, took a medical time out, returned and battled for another 16 games, all the while Hewitt was doing his best to run him off the court.
The Rod Laver Arena crowd, so used to cheering on their 'Aussie battler' Hewitt, rose to their feet to show Roddick the respect they felt he deserved.
In other men's second round action on day four, Spanish fifth seed David Ferrer, a semi-finalist last year, was taken to five sets by American Ryan Sweeting before prevailing 6-3 in the decider. He next faces Argentina's Juan Ignacio Chela, the 27th seed, who rolled to a 6-4 6-4 6-3 victory over Spain's Pablo Andujar.
Jo-Wilfried Tsonga , a finalist in Melbourne in 2008, recovered from an early deficit to beat Brazilian Ricardo Mello 7-5 6-4 6-4. Spain's Marcel Granollers, the 26th seed, was defeated by Portugal's Frederico Gil 6-3 4-6 6-4 6-3 who now meets the French sixth seed.
Serbian ninth seed Janko Tipsarevic came from a set down to oust Australian wild card James Duckworth 3-6 6-2 7-6 (5) 6-4 and will now face French 17th seed Richard Gasquet who led 6-4 6-2 3-0 when Kazakh Andrey Golubrev retired.
Rising Japanese star Kei Nishikori fought back from two sets down to defeat Australian Matthew Ebden on Margaret Court Arena. The 22-year-old dug deep to run out a 3-6 1-6 6-4 6-1 6-1 winner and now faces Julien Benneteau who won the all-French battle with 12th seed Gilles Simon 7-5 7-6 1-6 3-6 6-2.
Another Frenchman Gael Monfils, the 14th seed, beat hard-hitting Thomaz Bellucci 2-6 6-0 6-4 6-2 and now faces Mikhail Kukushkin after Viktor Troicki, the 19th seed, was sent crashing out in five sets by the Kazakh.