The victory sees Rune, ranked 40th in the world, become the first ever Danish man to reach the quarterfinals at Roland Garros, where he will face Norway’s Casper Ruud.
A former junior French Open champion, the 19-year-old is also the first man from Denmark to reach the quarterfinals of any grand slam tournament since Jan Leschly in 1967, according to the ATP Tour.
“I have an unbelievable feeling right now,” Rune said in his on-court interview after Monday’s match. “I was so nervous at the end, but the crowd was amazing for me the whole match, the whole tournament.”
He won a close first set against last year’s finalist Tsitsipas in just over an hour before the Greek leveled the match thanks to a break of serve at 4-3 in the second.
Rune regained the advantage with a break midway through the third set and raced into a 5-2 lead in the fourth to help close out the win.
Alongside Spain’s Carlos Alcaraz, Rune is the second teenager to reach the final eight of the men’s singles draw at this year’s Roland Garros, marking the first time two male teenagers have reached the quarterfinals of a major since 1994.
It caps off a stunning year for Rune, who gained his first win over a player ranked in the top five when he defeated Alexander Zverev at the Munich Open in April.
He will play Ruud on Wednesday after the 23-year-old defeated Poland’s Hubert Hurkacz 6-2 6-3 3-6 6-3.
Tsitsipas, meanwhile, becomes the highest-ranked player — and the first ranked inside the top eight in the world — to exit the men’s draw at this year’s French Open.