Djokovic extended his unbeaten run to 41 matches in 2011 as the Serb smothered dejected 13th seed Gasquet, who ran out of ideas during a 6-4, 6-4, 6-2 tennis lesson.
Djokovic will next face Italian Fabio Fognini, who came out on top in a four-hour-22-minute, five-set battle with Spain's Albert Montanes.
Should he beat Fognini he will equal John McEnroe's 42-0 record since the start of the year and set up a possible semifinal showdown with Federer. Federer, a 16-times grand slam champion, appeared to be floating through air in a 6-3, 6-2, 7-5 dismissal of fellow Swiss Wawrinka as he produced some delectable shots to draw "oohs" and "aahs" from the packed crowd. But barely anyone noticed women's third seed Vera Zvonareva make an early exit.
Zvonareva had to play in front of rows and rows of empty seats on Court Philippe Chatrier as she was knocked out by fellow Russian Anastasia Pavlyuchenkova 7-6, 2-6, 6-2 in a forgettable fourth-round contest.
The 14th seeded Pavlyuchenkova, at 19 the youngest woman left in the draw, reached her first grand slam quarterfinal after winning a topsy-turvy match filled with unforced errors and lost opportunities.
She will meet either champion Francesca Schiavone or three-times Roland Garros semifinalist Jelena Jankovic.
Zvonareva summed up the gloom surrounding women's tennis at this year's French Open, where none of the top three seeds reached the last eight for the first time since tennis turned professional in 1968, by saying: "It's not acceptable at this stage of the grand slam."
There was nothing, however, Gasquet could have done against Djokovic. The Serb was in a class of his own, barely blinking as Gasquet unleashed a series of his trademark sizzling backhands. But the ball would invariably come back. Faster.
Both players set up three break points each in the opening two sets, but while Djokovic saved them, Gasquet conceded two and folded in the third set.
Federer, the 2009 champion, barely put a foot wrong on the key points against Wawrinka and wrapped up victory on a sunsoaked court in less than two hours.
Fabio Fognini beat Spain's Alberto Montanes 4-6, 6-4, 3-6, 6-3, 11-9. Fognini saved five match points, one with a drop shot, as he fooled around on Court Suzanne Lenglen, notably pouring water on the trainer.
Sania-Vesnina advance
Sania Mirza and her partner Russian Elena Vesnina eased past Maria Jose Martinez and Anna Medina Garrigues in straight sets in the third round of the women’s doubles event. The seventh-seeded pair beat the Spanish duo, sseded eleventh, 6-1, 6-4 to move into the fourth round.
Indian veteran Mahesh Bhupathi’s campaign ended with a second round defeat in the mixed doubles event along with Chinese partner Jie Zheng. The fifth seed Indo-Chinese pair lost 6-4, 3-6, 7-10 to unseeded duo of Rennae Stubbs of Australia and Brazil’s Marcelo Melo. Bhupathi has already exited from the men’s doubles along with compatriot
Leander Paes.
Results (prefix denotes seeding): Fourth round: Men’s singles: 2-Novak Djokovic (Ser) bt 13-Richard Gasquet (Fra) 6-4, 6-4, 6-2; 3-Roger Federer (Sui) bt 14-Stanislas Wawrinka (Sui) 6-3, 6-2, 7-5; Fabio Fognini (Ita) bt Albert Montanes (Esp) 4-6, 6-4, 3-6, 6-3, 11-9. Women’s singles: Francesca Schiavone bt Jelena Jankovic (Ser) 6-3, 2-6, 6-4; Marion Bartoli (Fra) bt Gisela Dulko (Arg) 7-5, 1-0 (retd); 14-Anastasia Pavlyuchenkova (Rus) bt 3-Vera Zvonareva (Rus) 7-6 (7-4), 2-6, 6-2.
