Youzhny ended up with a 6-4, 0-6, 6-3 victory over Guillermo Garcia-Lopez. He managed to win just 10 of the 34 points in the second set but took nearly two-thirds of the points in the first and third sets.
The 2-hour match was the only one of Friday's four quarterfinals to go to three sets.
No. 3-seeded Martin Klizan pulled off a 6-3, 6-2 win over Ricardas Berankis in about an hour less time than Youzhny needed in his match. Klizan saved all four break points he faced and converted all four he had against Berankis.
Fourth-seeded Fabio Fognini topped Roberto Bautista-Agut 6-4, 7-6 (7-1) and Daniel Gimeno-Traver beat Flavio Cipolla 6-2, 7-5 in the other quarterfinals.
Saturday's semifinals will mark the first time Youzhny goes against Klizan. Fognini is 2-1 in his matches versus Gimeno-Traver.