Swiss star Roger Federer, the second seed, also won in straight sets, beating 15th-seeded Marin Cilic of Croatia 6-4, 6-3 to set up a quarterfinal against Jurgen Melzer or Nicolas Almagro.
"Today was another solid performance, which I'm very happy about," Federer said. "I think I was consistent and didn't allow him to get into the points he wanted to on my own serve." Nadal broke Gasquet's serve twice in each set, as the top-ranked Spaniard extended his winning streak at the clay-court tournament to 34 matches.
Nadal, who has lost his last three finals and is without a title since winning the Japan Open last October, felt he was far more aggressive than he was against Finland's Jarkko Nieminen on Wednesday.
"I feel when I'm playing well with the forehand, is very important shot for me. So I can have the control of the point most of the time," he said. "When I am playing well with the forehand, everything is a little bit less difficult." Nadal had a brief wobble when the 13th-seeded Gasquet picked up his form late in the second set, breaking the five-time French Open champion's serve with a superb crosscourt winner from the back of the court to level at 4-4.
But Gasquet, the former world junior champion who lost in the Monte Carlo semifinals to Nadal in 2005, hurried his shots in the next game going for spectacular forehand winners and Nadal broke back.
Nadal then closed out the match on serve when Gasquet's backhand pass bounced way out. The 24-year-old Nadal next faces former world No. 3 Ivan Ljubicic of Croatia.
"He's a very experienced player," Nadal said. "It's going to be a really difficult match tomorrow. I have to play like today if I want to have chances." The 16-time Grand Slam champion Federer once again looked sharp, just like he did when he beat Germany's Philipp Kohlschreiber in just 50 minutes in the second round.
Federer won 79 percent of first-serve points and 75 percent on second, breaking Cilic once in each set.
"I'm mixing it up well, using kick serves, slider, hitting it hard enough, making sure that, you know, I don't have to maybe go through that many second serves," the 29-year-old Federer said.
Third-seeded Andy Murray and fourth-seeded David Ferrer enjoyed comfortable wins on Thursday.
Murray saw off a hobbling Gilles Simon 6-3, 6-3. Frenchman Simon turned his ankle at the end of the first set and completed the match with heavy strapping on the injury.
The fourth-seeded Ferrer was far too experienced for 20-year-old Canadian Milos Raonic, winning 6-1, 6-3. The Spaniard dictated most of the rallies and pegged Raonic behind the baseline. The big-serving Raonic rarely threatened, managing only one ace and losing his own serve five times.
Ferrer nexts face eleventh-seeded Viktor Troicki of Serbia, who was trailing 3-6, 2-1 when Spaniard Tommy Robredo retired.
Ljubicic beat fifth-seeded Tomas Berdych of the Czech Republic 6-4, 6-2 to reach his third quarterfinal of the season.
Frederico Gil of Portugal, who came through the qualifiers, also reached the last eight after beating No. 8 Gael Monfils of France 7-6 (6), 6-2.
Gil's reward is a quarterfinal against Murray.
