Looking ahead to the remainder of the tournament, the Serbian admitted that he was pleased to have limited the time he spent on the court against Lorenzi.
"I tried to analyse my game, and my game was great from the start to the end," he told reporters. "It's also important for me to try to be as economical with the time I spend on the court as possible, but obviously not underestimating any opponent.
"I played really focused, tried to get to the net also. It was great all in all."
Djokovic will now take on Brazil's Rogerio Dutra Silva for a place in round three at Flushing Meadows.