The world No 23 and third seed saw off the Spaniard in two hours 15 minutes to earn a last-eight meeting with eighth seed Nicolas Mahut.
Mahut, one of a strong French contingent in the tournament, beat qualifier Ricardas Berankis of Lithuania 7-6 6-3.
Other victorious Frenchmen on Thursday were Edouard Roger-Vasselin and Michael Llodra, the 2010 champion and two-time runner-up at this event.
Sixth seed Roger-Vasselin beat Ukraine's Sergiy Stakhovsky 7-6 (7/2) 6-4, while Llodra ousted fourth-seeded Italian Andreas Seppi 7-6 (7/3) 6-4.
One of the home hopes to go out was seventh seed Julien Benneteau, who went down 4-6 7-6 (7/3) 6-3 to Germany's Jan-Lennard Struff.
Fifth seed Ivan Dodig from Croatia also made it through to the quarter-finals thanks to a 6-7 (4/7) 6-0 6-3 win over Germany's Tobias Kamke.
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