Gasquet, who is the higest seed left in the tournament following the exits of Marcos Baghdatis [ Images ], Gaston Gaudio and Dominik Hrbaty, was joined in the last eight by compatriots Sebastien Grosjean and Arnaud Clement [ Images ].
"I had to keep my concentration until match point," said French number one Gasquet.
"Now I have to face Robin Soderling [ Images ] who is one of the best players in the world on carpet. It will will be a very difficult game."
Clement, winner of the event in 2000 but now ranked 50th, defeated fellow Frenchman Michael Llodra 2-6, 6-1, 7-6.
Sixth seed Grosjean was a 7-6, 6-2 winner in another all-French encounter against Cyril Saulnier.
Grosjean, ranked 30th in the ATP standings, had to save a set point in the opening set before strolling through the second set.
"Cyril played a very good game. I think I was a bit lucky to break him when he was serving for the set at 6-5," said Grosjean, who will face compatriot Marc Gicquel in the quarter-finals.
"I played better afterwards and two passing-shots gave me the win."
Seventh seed Xavier Malisse of Belgium also reached the quarter-finals through a 6-2, 7-6 win over Frenchman Julien Benneteau [ Images ].
He will play American Robby Ginepri, who crushed German Simon Greul 6-1, 6-2.

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