Nardi, who grew up idolizing Djokovic and is ranked 123rd in the world, played the match of his life to defeat the Serbian, dropping his racket and putting his hands over his face after firing an ace out wide to seal the win.
The defeat ends Djokovic's bid for a record sixth title at the tournament in the California desert.
"This is a miracle," said Nardi, who lost to David Goffin in qualifiers on Tuesday and only got into the main draw after Tomas Etcheverry withdrew due to injury.
"I'm a 20-year-old guy, 100 in the world and I beat Novak. Crazy. Just crazy."
Nardi came out flying under the lights on centre court, drawing Djokovic to the net with a short ball and then rifling a forehand past him for an early break and a 3-2 lead.
Djokovic was well short of his best and a service return from the 24-time Grand Slam champion found the net to hand Nardi the first set.
The top seed broke Nardi twice in the second set and held at love to level the contest but his opponent, who had a poster of Djokovic on his wall growing up, refused to back down.
Nardi hit a backhand that Djokovic could not put back in play for a crucial break and a 4-2 advantage in the decider before pulling off the upset.
He will next face American Tommy Paul.
Earlier, Gael Monfils produced a stunning display of shot-making and showmanship to rally from a set and 3-0 down to beat former champion Cameron Norrie 6-7, 7-6, 6-3 to reach the last 16.
The 37-year-old Frenchman electrified the crowd with his creativity to set up a fourth-round meeting with ninth seed Casper Ruud.
Norrie, who won the tournament in 2021, piled up 60 unforced errors and could not solve the unpredictable Monfils puzzle in the three-hour and 15-minute affair.
"I feel better and better, to be honest," said Monfils, who was sidelined with a wrist injury for part of last season.
"I've been playing weeks after weeks, which has been a long time I am able to do that. I feel good. So far the body is holding, so I'm happy with that."
American Taylor Fritz, the tournament's 2022 champion, breezed past Sebastian Baez 6-2, 6-2 and Grigor Dimitrov's career renaissance got another big lift with a 6-3, 6-3 win over France's Adrian Mannarino.
Seventh seed Holger Rune beat Lorenzo Musetti 6-2, 7-6 and 17th-seeded American Paul sailed past Ugo Humbert 6-4, 6-4 in other third-round action.
