The defending champion wasted little time against the outgunned Italian, taking just 73 minutes to wrap up the win, and said that while it was important to approach each match with the same professional attitude he also wanted to enjoy his time at Flushing Meadows.
The Serbian second seed, who also lost just two games to Lorenzi in the opening round of the Australian Open this year, said he revelled in the electric atmosphere of night matches in New York.
The Serb has danced on court in the past, worn a cap from the New York Fire Department and generally tried his hardest to get the raucous crowd on side.
Djokovic described Arthur Ashe Stadium as the most exciting tennis arena in the world and said he felt obligated to entertain as well as win.
"Yes we need to be professional, committed, focused on what we do," he said. "Our profession brings us a lot of success. A lot of pressure, important moments, a lot of challenges, but also a lot of joy.
"I always try to take everything from a bright, positive side. It's very important to embrace whatever life brings you. I'm fortunate because I have a great team of people around me. That's where there's a great source of positive energy for me. We try to joke around all the time. That's us."
Former champion Andy Roddick gave young American Rhyne Williams a harsh introduction to Grand Slam tennis as he breezed to a 6-3 6-4 6-4 victory.
The 29-year-old, whose only Grand Slam title to date came in 2003, banged down 20 aces as he claimed victory on a sweltering day at Flushing Meadows.
Williams, a qualifier ranked 289th in the world, gave a good account of himself on the vast Arthur Ashe Stadium court but Roddick had too much experience and class for him.
The 20th seed now meets Australia's Bernard Tomic, who beat Carlos Berlocq of Argentina 4-6 7-5 6-3 6-4.
Fifth-seed Jo-Wilfried Tsonga beat qualifier Karol Beck 6-3 6-1 7-6 (2) despite being a break down in the final set.
Sixth-seed Tomas Berdych also moved on in straight sets despite some tricky moments against David Goffin 7-5 6-3 6-3.
Juan Monaco, the 10th seed was ousted in a lengthy five-setter by Guillermo Garcia-Lopez, the Spaniard winning 3-6 1-6 6-4 7-6(6) 7-6(3).
Fourteenth seed Alexandr Dolgopolov was also taken all the way, the Ukrainian finally recovering from a sluggish start to come back from two sets down and beat Jesse Levine of the US 3-6 4-6 6-4 6-1 6-2.
There were no such problems for Julien Benneteau of France, the 31st seed overcoming Olivier Rochus in straight sets 7-6(1) 6-2 6-3.
Nicolas Almagro, seeded 11th, beat Radek Stepanek 6-4 6-7(5) 6-3 6-4 and Stanislas Wawrinka, the 18th seed, beat Sergiy Stakhovsky 6-7(6) 7-6(2) 6-4 6-2 to secure their places in the second round.
Milos Raonic survived a huge scare before finally coming through against Santiago Giraldo 6-3 4-6 3-6 6-4 6-4. The 15th-seeded Canadian could meet Andy Murray in the fourth round.
And Sam Querrey of the US downed Lu Yen-Hsun of Taiwan to progress into the second round, the 27th seed winning 6-7(4) 6-4 6-4 7-5.