The German won the tie 6-4, 6-4, 4-6, 7-6 (9-7) in three hours and eight minutes of adrenaline fueled tennis.
Djokovic and Nadal met in the semi-final of the competition last year, which saw the Serb emerge victorious after an epic battle.
Nadal came into the French Open with little experience on clay, having only played five matches on the surface this year.
Djokovic was aiming to keep his perfect record against the Argentine, but as he went out of the tunnel onto the court, he discovered that not was on the same page.
The King of Clay advanced to the quarter-final where he will face world no. 1 Novak Djokovic, who beat Diego Schwartzman in straight-sets.
US tennis player and 11th seed Jessica Pegula emerged victorious in her third round match against Tamara Zidansek.
Diego Schwartzman won just three games against Dimitrov in the second round of the ATP Masters 1000 tournament earlier this month.
During the post match press conference, the German discussed the importance of social media on a tennis player's career.
In an earlier interview with ATP, the Dutchman had said that Rafa was one of his idols, someone he was hopeful of meeting.
US tennis player and ninth seed Danielle Collins said her goodbyes as well after losing to compatriot Shelby Rogers.