By SABC Sport
18th May 2023
The young Dane came through 6-2 4-6 6-2 against the defending champion in a rain-hit encounter in Rome.
Seventh seed Rune raced through the opening set in 39 minutes before Djokovic was seen to by the physio early in the second and given some medication before the weather forced play to be suspended.
Top seed Djokovic - who beat Britain's Cameron Norrie in a feisty fourth-round match - levelled the match soon after the resumption, but it was Rune who pulled clear in the decider.
Rune, making his tournament debut, opened a 4-0 lead after a double break before closing out the match for successive victories in his matches against the Serbian.
"It's really a big win for me," Rune said in his on-court interview.
"Obviously I did it last year in Paris as well, but every match is a huge challenge for me when I play against Novak.
"He is one of the greatest that's ever played the game. I knew I had to be at my best and I said it yesterday, and I was today.
"I am super proud of myself and I enjoyed every moment out there, but I stay humble of course. I have a lot to achieve."
Both players had clashed with chair umpire Mohamed Lahyani during the match.
World number seven Rune was less than impressed with a line call during the second set from Lahyani, who was involved in a row with Britain's Andy Murray in his first round defeat by Fabio Fognini. "You're an absolute joke man," the Dane said.
Djokovic then lost his cool over the delay in which Lahyani gave out the score in Italian and then English.
"What are you acting here or what? Why do you call the score for 20 seconds? Just call the score. For God's sake," said Djokovic, who had been warned about exceeding the maximum time of 25 seconds between points.
Djokovic will now turn his attention towards the French Open, which starts on May 28. "I know I can always play better," he said, quoted on the ATP Tour website.
"Definitely I am looking forward to working on various aspects of my game, of my body, hopefully getting myself in 100 per cent shape, that is the goal.
"I always like my chances in Grand Slams against anybody on any surface, best-of-five, so let's see how it goes."
Reflecting on his defeat to Rune, the world number one said: "He was just better. He played too good for me for most parts of the match.
"I did have a bad start of the third set. I think that's where the match kind of shifted to his side. He kept his nerves and deserved to win."
Rune will play Casper Ruud in the semi-finals after the forth seeded Norwegian beat Francisco Cerundolo 7-6 (5) 6-4.
In the women's singles, world number one and top seed Iga Swiatek was forced to retire in her quarter-final against reigning Wimbledon champion Elena Rybakina.
With the scores level at 2-2 in the deciding set, Swiatek pulled out through injury. The Pole won the first set 6-2 before Rybakina took the second-set 7-6 (3) in a tie-break.
Swiatek had been bidding to make it 15 straight wins at the Italian Open, while Rybakina will now face Jelena Ostapenko, who booked her place in the semi-finals with a 6-2 4-6 6-3 win over Paula Badosa.