This victory allows Rune, ranked 40th in the world, to become the first Dane to reach the quarter-finals at Roland Garros, where he will face the Norwegian Casper Ruud.
A former French Open junior champion, the 19-year-old is also the first Dane to reach the quarter-finals of a Grand Slam tournament since Jan Leschly in 1967, according to the ATP Tour.
“I feel amazing right now,” Rune said during his on-pitch interview after Monday’s game. “I was so nervous at the end, but the crowd was amazing for me the whole game, the whole tournament.”
He won a tight first set against last year’s runners-up Tsitsipas in just over an hour before the Greek leveled the game with a break of serve at 4-3 in the second.
Rune regained the lead with a break midway through the third set and took a 5-2 lead in the fourth to help wrap up the win.
Alongside Spain’s Carlos Alcaraz, Rune is the second teenager to reach the last eight of the men’s singles draw at Roland Garros this year, marking the first time two teenage boys have reached the quarter-finals of a major tournament since 1994. .
It caps off a stunning year for Rune, who picked up his first victory against a top-five ranked player when he defeated Alexander Zverev at the Munich Open in April.
He will face Ruud on Wednesday after the 23-year-old beat Poland’s Hubert Hurkacz 6-2 6-3 3-6 6-3.
Tsitsipas, meanwhile, becomes the highest-ranked player – and the first among the top eight in the world – to drop out of the men’s draw at this year’s French Open.