Youzhny was just two points from elimination in a pivotal second-set tie-break in his second-round encounter with the world No.6 and second seed, but recovered to win 2-6 7-6 (8/6) 6-4.
Third-seeded Czech Tomas Berdych edged out Andrey Kuznetsov 6-3 2-6 7-6 (7-4) while seventh seed Viktor Troicki set up a quarter-final clash with US Open champion Stan Wawrinka by beating fellow Serbian Dusan Lajovic 6-4 6-4.
At the Moselle Open in Metz, two former champions in David Goffin and Gilles Simon secured their last-eight places with victories over Jan-Lennard Struff and Guillermo Garcia-Lopez respectively.
Goffin, the second seed, lost just 10 services points as he eased through 6-4 6-2 in 67 minutes while Simon, a two-time event winner, came through 6-7 (5-7) 3-6 6-4.
Third seed Lucas Pouille saw off fellow Frenchman Pierre-Hugues Herbert 6-4 6-7 (6-8) 6-4 while Nicolas Mahut came through 6-3 6-4 against Ukraine's Illya Marchenko.
