Paris-born American Cressy won 7-5 6-7 (3-7) 7-6 (7-4) in a little over two and a half hours on Saturday, countering 10 double faults with 15 aces on his way to victory.
Rune, the Danish 19-year-old who sits ninth in the world rankings, had won his three previous matches against Cressy, including a second-round clash at the Australian Open last month, but he could not extend that dominance at the indoor event in Montpellier.
It means Cressy faces second seed Sinner, who beat 18-year-old French wildcard Arthur Fils in the first semi-final, ending the teenager's eye-catching run with a 7-5 6-2 victory.
Fils had beaten Richard Gasquet and Roberto Bautista Agut on his way to the last four but found world No.17 Sinner was more than his match.
Last year saw Sinner reach just one ATP final, taking a title on clay in Umag, after making it through to five title matches in the 2021 season.
He had his best year at the grand slams, however, reaching quarter-finals at three of the four majors.
Cressy recognises the threat posed by the Italian, saying in an on-court interview: "Jannik Sinner is an incredible player, just like Holger Rune and everyone else in the tournament. I believe you've just got to bring your 'A' game every time and I'm really looking forward to it."
Competing well in France has been pleasing for Cressy, who is set to climb from 51st in the rankings and into the top 40 on Monday.
"I lived and grew up here, and I'm extremely happy," Cressy said.
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