"It's great to be back here in Melbourne where I have the nicest memories of my tennis experience," Djokovic said.
"This is the grand slam I've won twice, I always play well here."
Djokovic came into the tournament following a holiday and without an official match under his belt in 2012, but there was little evidence of rustiness.
"I wanted to have that period of preparation to really get ready for the Australian Open," he added.
"Physically I think I'm stronger, I'm improving things by small margins. It's something that gives me a lot of confidence."
Lorenzi tested the world number one as best he could, but Djokovic was certainly up for the challenge.
He did suffer the occasional lapse in concentration, notably in the third game of the opening set when a double fault and a low volley into the net gifted Lorenzi the first break of the match.
However, Djokovic is nothing if not a perfectionist and tightened his game to break the Italian three times on his way to claiming the first set.
A lengthy and powerful duel in the opening game of the second set left the crowd anticipating a baseline battle for dominance, and while Djokovic was stretched, it was never too far as he swept through the set 6-0, winning it with a perfect forehand down the line.
Lorenzi never gave in, but found no answers to Djokovic's commanding arsenal or silky drop shots, powerful baseline play and skilfully placed volleys.
With the temperature hovering around 35 degrees on Rod Laver Arena, Djokovic was no doubt happy to wrap the match up in just over 90 minutes.
"Today was around 35 degrees so it took a bit of time to get used to the heat. Still I am quite happy with how I'm handling it physically."
As for the match, he added: "It took me a couple of games to find my rhythm but I think I played well after the first set."
Djokovic used the lack of genuine competition to experiment, making regular excursions to the net.
"When you're 3-0, 4-0 up why not try some other things, some things that are not usual characteristics of your game," he said.
"I am definitely working on my net game and am trying to approach the short balls as much as I can and take my chances."