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In the process, former Paris Masters champion Rune gave his own slim qualification hopes a boost, battling past the Australian in a match that lasted two hours and 28 minutes.

It was a baselune slugfest in the French capital, and ultimately it was De Minaur's serve that let him down.

He made just 47 per cent of his first serves throughout the tussle, and Rune's relentless attack would prove the difference, the Dane firing 24 winners past De Minaur and recovering from a break in the deciding set to claim victory.

"He was putting so much up against me. He was making every ball with quality, deep in the court and the court is quite fast here," Rune said of De Minaur.

"I had to adjust my game a little bit and it was a constant battle but how I treated the last couple of games was very good. I went for it, I got it and I am very happy."

Rune sits 13th in the rankings on 3,025 points and can still qualify for the ATP Finals.

Eighth-placed De Minaur, who has 3,745 points, currently occupies the final qualification spot and is still aiming to make his debut in Turin despite this loss.

However, if Rune goes on to win a second Paris title in three years – he beat Novak Djokovic in 2022 to claim his first –  he would move to within 120 points of De Minaur.

But the dream of becoming the first Australian to qualify for the season-ending showpiece is not dead yet, and De Minaur will go on the hunt for more points at the ATP 250 event in Belgrade next week.