Djokovic had few problems in winning 6-2, 6-0, 6-0 and will next play Colombia's Santiago Giraldo.
The Serbian world number one broke Lorenzi's service nine times in wrapping up his opening match in 1hr 32min on a sweltering day on Rod Laver Arena.
Such was the lack of pressure that Djokovic even had the opportunity of playing a trick shot through his legs that Lorenzi netted.
Djokovic is bidding to become just the fifth man to win three consecutive Grand Slam titles in the Open Era joining Rod Laver, Pete Sampras, Roger Federer and Rafael Nadal.
Last year's Australian Open final triumph over Andy Murray was the first of seven straight tournament wins in a 41-match winning streak that was finally ended by Federer in the semifinals of the French Open.
Djokovic, 24, won a career-best 10 titles in 11 finals last year. He defeated world number two Nadal six times and overall was 21-4 against top-10 opponents.
