Simon, seeded No. 2 this week, edged Jarkko Nieminen 4-6, 6-4, 6-4. He recorded three breaks in the final set and needed them as he dropped serve twice.
Simon also lost his serve twice in the first set in falling behind but saved both break points he saw in the second set to even the match. He then won 56 percent of the points off Nieminen's serve in the third set for the win.
He'll next go against Daniel Brands, who built a 7-6 (7-1), 2-0 lead on Gael Monfils before Monfils retired from the match.
Lukas Rosol eliminated third-seeded Andreas Seppi 6-1, 3-6, 6-3 and No. 8-seeded Viktor Troicki stopped Tobias Kamke 6-4, 6-2 with three breaks in each set. Troicki and Rosol are to meet in the quarterfinals.