The world number one is renowned for his will power and stamina but conceded his title defence had been on shaky ground when his Italian opponent took a two sets to one lead during the four-and-a-half hour match.
"I was in real trouble on the court and he was playing some really amazing tennis. I didn't know really what to do," the Serb said.
"From both hands, he was getting a lot of balls back, winners from both corners. Good serves running every ball down the court. It didn't feel great playing him that third set and the beginning of the fourth.
"The (crowd) start chanting my name and I just felt a great new wave of willpower and energy. I really needed that push, I really needed that energy.
"I think I was a different player from that moment onwards. And I think from that moment, I probably lost only one game in the rest of the match. I was on a high, riding that wave."
Defeat would have ended the Serbian's quest for a record-extending 25th Grand Slam trophy and resulted in him losing the number one ranking to Musetti's compatriot Jannik Sinner later this month.
Djokovic might have had grounds for complaint after organisers had wedged another contest into the evening schedule, pushing the completion of his match to 3:06 a.m., the latest ever finish at the French Open.
The three-time French Open champion preferred to focus instead on the quality of the five-set contest.
"I don't want to get into it. I have my opinions but I think there are great things to talk about in this match today," he said.
"Both Lorenzo and my performances stand out so I don't want to be talking about the schedule. I think some things could have been handled a different way but there's also a beauty in winning a match (so late)."
Djokovic, who said on court that he would not able to sleep because of the adrenaline rush, will be back in action on Monday in the fourth round against Argentine 23rd seed Francisco Cerundolo.
"I really physically, pushed myself to the very limit to win this match," he said.
"I'm going to have to switch on all my young genes and try to recover as quickly as possible."