Third seed Klizan will face Fabio Fognini in Sunday's final after the fourth-seeded Italian beat Spain's Daniel Gimeno-Traver 6-3 6-4 in the first semi-final.
Klizan, the world number 45 from Bratislava, led Youzhny 5-2 in the final set but wobbled serving for the match, allowing the 29th-ranked Russian to level the contest and force a tiebreak.
However, the more-experienced Youzhny, who won the first set tiebreak 13-11, double-faulted early on to gift his 23-year-old opponent a mini-break and never recovered.
Klizan fired a forehand down the line on his first match point to seal victory after three hours 49 minutes.
"It was a very, very difficult match," said Klizan, who did several push-ups on the court right after his triumph as if to show that he is in top physical shape.
"I was fighting the whole match. I feel sorry for Mikhail because he is from Russia and people wanted to see him in the final but I really wanted to win this match."
Fognini's path to the final was more straightforward even if he had to overcome a poor start before taking control.
"Daniel started well, breaking me in the first game but I was able to break back and then manage another break. The second set was also tough," Fognini told reporters.
"Now, I'm in a final and I could dream of winning it," added the Italian, who lost to France's Gilles Simon in his only previous title match in Bucharest this Apr
- Fabio Fognini