Jordan Thompson's first appearance in a Masters 1000 quarter-final also ended in disappointment as a partisan crowd cheered home his French conqueror Ugo Humbert in Bercy on Friday night (Saturday AEDT).
Jordan Thompson's dream run at the Paris Masters was ended by popular local Ugo Humbert. (AP PHOTO)
The duo had been only the second Australian men's pair in the last 20 years to get to the last-eight of the singles in the same Masters event after Alexei Popyrin and Max Purcell in Cincinnati last year.
But just as his hopes up the road at Roland Garros in the French Open had been ended at the quarter-final stage earlier in the year, de Minaur again bowed out at the same point in the French capital 6-4 4-6 7-5 after an engrossing two-hour 25-minute slugfest with Rune, a player who shares his fighting qualities.
But, ultimately, the 21-year-old Dane saved his best for last in the dying stages of Friday's absorbing contest to set up a semi-final with Alexander Zverev, the German who had ended de Minaur's quest at the French Open.
The silver lining for de Minaur may still yet be a coveted first-time place in the ATP Finals in Turin later in November.
For the Australian No.1 departs the tournament provisionally still holding onto the eighth and final place for the Finals in Turin, while still knowing there's a danger he could yet be surpassed by his chasers in the final furlong of the race in next week's final qualifying events in Belgrade and Metz.
Andrey Rublev, who will be competing in Metz, is just 25 points behind de Minaur in ninth, but 10th placed Grigor Dimitrov, looking tired after his recent exertions, blew his chances in the day's late match when he lost 6-2 6-3 to the in-form former Paris champ Karen Khachanov.
Rune could still chase down de Minaur in the race, but he will have to regain the Paris title he won in 2022 and go on a big run too in Metz next week.
Later on Friday evening, Thompson, in uncharted waters after reaching a Masters quarter-final for the first time in 28 attempts stretching back seven years, cut a lonely figure as the Paris crowd again went crazy for the wild-eyed Humbert, still on a high after stunning Carlos Alcaraz 24 hours earlier. Â
The dashing left-hander overcame an injured foot and a stirring late rally from the 30-year-old Thompson to power through 6-2 7-6 (7-4) while being helped by 23 winners to set up his semi-final meeting with Khachanov.
Denmark's Paris specialist Holger Rune celebrates his win over de Minaur. (AP PHOTO)
Zverev, who's already guaranteed a place in Turin, had earlier advanced to the semis against Rune by beating Stefanos Tsitsipas 7-5 6-4, in the process killing off the Greek's last faint hopes of making the ATP Finals.
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