Youzhny, the 2004 champion and a two-time runner-up, managed only five points on his serve in the second set but recovered after an early break in the third set and won four consecutive games for a 5-2 lead. He landed a high volley down the line to earn two match points and wrapped up the victory with a low volley at the net.
"If I cut off the second set, I can say that I'm satisfied with the level of my tennis and the result of the match," Youzhny said. "The first set was a really tough one and my current physical form was not enough to play the whole match on a high level."
The Russian will next face Klizan, who eliminated Ricardas Berankis of Lithuania 6-3, 6-2. The 45th-ranked Klizan, who mostly plays on the Challenger Tour, saved four break points and broke Berankis twice in each set to reach his second career semifinal.
Fognini defeated Roberto Bautista-Agut of Spain 6-4, 7-6 (1).
"I broke him just one time in the first set but it was a tough set," Fognini said. "I was 5-3 up in the second set but he (Bautista-Agut) played three perfect games. I was serving for the match at 6-5 down and won that game, which was very important. And I then served well at the tiebreaker and won it easily."
The Italian won his first title in Bucharest, Romania, in April. In his second semifinal appearance this season, Fognini will play Gimeno-Traver. The Spaniard eliminated Flavio Cipolla of Italy 6-2, 7-5 to reach his first semifinal in more than two years.