Shelton won 7-5 6-7 (7-3) 6-4, saving the six break points he faced, and converting the only two he forced in Friday night's match in Basel.
The American reached his fifth semi-final from nine quarters this year.
"I struggled a lot this year in quarter-finals and I've lost a lot of them against top 10 players," Shelton said.
"It's been a tough hump to overcome. To get to the second-to-last week of the year and finally do it is huge for me. Especially with the way I was able to overcome everything Rublev threw at me."
The American will face one of his best friends on tour, Arthur Fils of France, whom he lost to last month in the Tokyo quarter-finals.
"There is no one I would rather match up against on a Saturday here in Basel," Shelton said. "I'm looking for some revenge."
Fils defeated third-seeded Stefanos Tsitsipas 7-6 (7-5) 6-3 and improved to 2-0 against the Greek.
"I served pretty well," Fils said. He won 88 per cent of his first serve points and has yet to drop a set.
Also yet to drop a set was fourth-seeded Holger Rune, who defeated lucky loser David Goffin of Belgium 6-2 6-4.
Rune's semi-final opponent is Giovanni Mpetshi Perricard of France, who served 27 aces and hit 46 winners but broke Denis Shapovalov of Canada only once.
Mpetshi Perricard won their first matchup 6-7 (9-7) 6-3 7-6 (7-3) after keeping Shapovalov in the serve-fest with 37 unforced errors.
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