Djokovic's last meeting with Musetti on clay was a gruelling Roland Garros clash in 2021, in which he battled back from two sets down to win, but this time it was the Italian that claimed a comeback victory in windy conditions.
Both players struggled on their serve in a contest littered with 15 breaks of serve, but Djokovic appeared to have the match in hand as he comfortably took the first set.
However, Musetti refused to go down without a fight and the Italian stepped on the gas in the second set to level the topsy-turvy encounter.
Not even a lengthy halt in play due to rain could dampen Musetti's momentum, and the 21-year-old once again took advantage of a weak serving performance from Djokovic to break and take the win.
"I'm struggling not to cry. It was a really long match, not easy conditions. It was a bit windy, cold," Musetti said. "I'm really proud of myself. The rallies were long, it was a tough, physical battle. Beating Novak is something remarkable for me."
Musetti will next face fellow Italian Jannik Sinner, who beat Hubert Hurkacz.
In the last act of the evening, Medvedev continued his impressive form this season with a 3-6 7-5 7-6(7) thrilling win over Zverev in the 14th chapter of their long-running rivalry.
A month after defeating Zverev in the last 16 at Indian Wells, the winner of four hardcourt titles this year recovered from a set down to beat the German once again in what was his first clay clash.
After winning the first set, Zverev was 5-4 serving for the match in the second when Medvedev earned a crucial break and won three straight games to force a decider.
The 27-year-old Russian claimed his 31st win of 2023 after saving two matchpoints in a dramatic tiebreak.
"That was a crazy match," said Medvedev. "He served two times for the match, but that is also clay courts. You can come back at any moment.
"The serve doesn't count as much, so as soon as someone gets a little bit tight, the match can turn around in one second. That's what I managed to do."
Seventh seed Sinner was made to toil by Hurkacz in a 3-6 7-6(6) 6-1 win.
Watched on by sprint great Usain Bolt in the stands, Hurkacz raced to a 3-0 lead before Sinner got on the board and the world number 13 wobbled towards the end of the opening set before wrapping it up with two fiery first serves.
Sinner, a Monaco quarter-finalist last year as well, found himself in more hot water shortly after the second set began but the Italian hit back after dropping serve to grab a break and level at 2-2.
Hurkacz raised his game to force a tiebreak and looked in control but the scrappy Sinner saved a matchpoint and dragged the contest into a decider. The Italian then got his nose in front and held firm to complete the win as Hurkacz faded.
German qualifier Jan-Lennard Struff earlier stunned fourth seed Casper Ruud 6-1 7-6(6), ending the Estoril champion's nine-match winning streak on clay stretching back to last July.
World number one Novak Djokovic meets Lorenzo Musetti as he continues his quest for a record-extending 39th Masters trophy and builds momentum ahead of the French Open, while defending champion Stefanos Tsitsipas will play Nicolas Jarry.
In-form third seed Daniil Medvedev, the winner of four hardcourt tournaments in 2023, will take on Alexander Zverev in the pair's first claycourt meeting.
Italian Matteo Berrettini earlier withdrew from his meeting with sixth seed Holger Rune due to an abdominal injury, sending the Danish teenager through to the last eight.
