The match started in surprising fashion as Lorenzi shocked the crowd in New York to break Djokovic's serve in the opening game of the contest.
Djokovic replied to the early setback superbly and quickly built a lead in the first set by punishing some poor serving from his Italian opponent.
Lorenzi failed to win another game in the set, with Djokovic taking a lead after a 6-1 triumph.
The Serb was in full flow in the second set, breaking Lorenzi's serve on three occasions to extend his lead with a 6-0 win.
Djokovic was once again able to secure a break of serve early in the third set and the former world number one's class from the back of the court was often too much for Lorenzi to handle.
More errors from Lorenzi late on allowed Djokovic to finish the match inside 90 minutes with a 6-1 victory in the third set to move into round two of the final major tournament of the year.