Gasquet hit 10 aces and saved all six break points he faced. The World No. 15 also reached the last eight at the Apia International Sydney (l. to Istomin), the Open Sud de France in Montpellier (l. to Kohlschreiber) and the ABN AMRO World Tennis Tournament in Rotterdam (l. to Davydenko).
"I served well today and played good during the important moments," said Gasquet. "If I continue like this, I can go further in the tournament. I'm playing solidly and feel well this week. This is a great tournament and I always like coming back here."
Looking ahead to a quarter-final against either Juan Martin del Potro or Nikolay Davydenko, Gasquet said, "They both played very well in Rotterdam, they are two great players."
France's Michael Llodra, the 2010 champion and 2009 runner-up, knocked out sixth seed Alexandr Dolgopolov of the Ukraine 6-4, 5-7, 7-6(5) in two hours and 20 minutes.
Llodra, who led 5-2 and 6-3 in the tie-break, hit 19 aces and saved six of nine break points. Dolgopolov, last month's Brisbane International finalist (l. to Murray), dropped to a 7-4 record on the season.