World number eight Rudd, who claimed the title in Geneva last year with a straight-sets final win over Denis Shapovalov, overcame Kokkinakis 6-4 7-6 (7-3) on Thursday and will now face Opelka.
The American bounced back from losing the second set against Dutchman Tallon Griekspoor to claim a 6-4 3-6 6-3 win as he bids for his third title of 2022, and second seed Ruud said he was excited to pit himself against Opelka after securing his spot in the semi-finals.
"I expect it to be tough," Ruud said. "But I will do my best and see how I can do. I always enjoy playing against Reilly. He is a similar age to myself, and it will be another battle against him – hopefully it will be a good one."
Elsewhere, three-time grand slam semi-finalist Richard Gasquet followed up his shock win over Daniil Medvedev with a 6-2 6-4 victory over Kamil Majchrzak, and will face Joao Sousa for a place in the final after the Portuguese beat Ilya Ivashka 7-5 7-5.
At the Lyon Open, top seed Norrie battled to a 6-4 4-6 7-5 win over Sebastian Baez, spurning three match points before finally downing the Argentinian after a marathon two hours and 40 minutes clash.
The world number 11 will face Holger Rune in his semi-final contest after the 19-year-old came from a set down to beat Manuel Guinard 3-6 6-3 6-4.
The other semi-final in France will see fourth seed Alex de Minaur take on Alex Molcan after the Australian's quarter-final opponent Yosuke Watanuki withdrew after losing the first set 6-4, citing a back issue.
Molcan, meanwhile, downed Federico Coria 6-3 6-2 to reach the final four.