The pair had met at the same stage in a bad-tempered match in 2022 with Ruud emerging victorious in four sets before falling in the final to 14-time champion Rafael Nadal (37).
While this year's Scandinavian clash lacked the vitriol, it was equally captivating even though it had looked one-sided at the start.
Sixth-seed Rune, who had beaten Ruud at the Italian Open last month, littered the court with 26 unforced errors in the first two sets.
It was all business for Ruud, who will play Alexander Zverev (26) on Friday, and he broke the young Dane in the second game to go 3-0 up.
It got even worse for Rune when two consecutive double faults and a forehand into the net gave Ruud another break to go 5-1 up before he sealed the first set a game later.
Rune sank an easy smash into the net to drop serve in the very first game of the second set.
His opponent was a model of consistency early on, keeping unforced errors to a minimum and forcing his younger rival to make them instead.
Another easy forehand into the net by Rune gave Ruud a 4-1 lead before he quickly moved two sets up.
The Dane, however, was not done yet, snatching his very first break at the start of the third to turn the tables.
With loud screams and shouts of 'come on' after every single winning point, Rune clinched the third set, having added considerable power to his baseline game.
But the Norwegian recovered and got his revenge with an early break, moving 4-1 clear. Another Rune double fault gave his opponent his first match point at 5-2. He missed another before sealing it on his serve with his fifth opportunity.
Check out the game summary with Flashscore.
