For all the disappointments in his career, Monfils is usually at his best in Paris.
Fourth seed Gael Monfils of France takes on Belgian Olivier Rochus in his first match.
Eighth-seeded Tomas Berdych of the Czech Republic also advanced, beating Gael Monfils of France 6-3, 6-2.
Simon struggled to display his best form following an exhausting four-and-a-half-hour win against Gael Monfils on Saturday.
Nadal will next face 12th-seeded Frenchman Gael Monfils for a place in the semifinals of the tournament.
Second seed Stepanek won 6-2 6-1 against Frenchman Gael Monfils, who was struggling with a shoulder problem.
But as Monfils has shown, patience just might be the most important skill at this year's French Open.
After opening a two-set lead, Monfils saw world number 12 Ferrer claw his way back to two sets apiece.
Earlier on Tuesday, France's Gael Monfils made the third round with a 6-4 6-4 win over Argentine Juan Monaco.
"Deep inside my dream is to win a Slam and deep inside I know I can make it, " Monfils said.
Baker won three qualifying matches to reach the main event, and beat No. 84-ranked Sergiy Stakhovsky to get to Monfils.
France's hopes of a first men's champion in 30 years remained on course with further victories for Jo-Wilfried Tsonga and Gael Monfils.
Monfils responded with lunging forehands, drop shots, booming serves and touch volleys.
He was joined in the last four by third-seeded Frenchman Gael Monfils, who receovered to beat American James Blake 3-6 6-3 6-4.
In Wednesday's quarter-finals, Federer will face Sweden's Robin Soderling, the fifth seed, while third seed Novak Djokovic takes on Frenchman Gael Monfils.
Monfils fought hard in the first set but ended up well beaten.
Tsonga, who is working with Roger Rasheed, Monfils's former coach, said the additional pressure of being French at the French Open motivated him.
That year he lost to Roger Federer, who could be his opponent in the semifinals this year if Monfils gets that far.
However, Monfils, ranked 17th in the world, regained his nerve in the next game to break back and put his country 1-0 up.
In the middle of it all, Monfils asked the chair umpire for permission to take an iPhone video of the crowd doing the wave.
The world number 35, who knocked out ninth seed James Blake in the third round, pressured Monfils from the start by attacking whenever possible.
Michael Llodra beat Fernando Verdasco 6-7 (5-7), 6-4, 6-3, 7-6 (7-2) after Gael Monfils prevailed 7-6 (7-3), 6-2, 4-6, 5-7, 6-4 against David Ferrer.
World No. 15 Monfils beat Australia's Marinko Matosevic 7-6 (7-5) 6-3 6-3 to earn a tie with Brazil's Thomaz Belluci, who eliminated Israel's Dudi Sela.
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Fish, who had never gone beyond the second round at Flushing Meadows before this year, struggled with his serve against Monfils but volleyed superbly throughout.
Monfils struggled to deal with Fish's tactics, which involved him getting to the net at every opportunity, and many of the American's 49 winners were smashes.
And when Monfils failed to serve out the match at 5-3 in the fifth, it seemed like the momentum had swung back in the Spaniard's favour.
He won his first two qualifiers but was beaten in the third before a late reprieve after home hope Gael Monfils pulled out due to injury.
Federer will face Gael Monfils or David Ferrer in the last eight, with the Frenchman leading 6-4 2-6 7-5 0-2 when bad light stopped play on Sunday.
Monfils, a 6-4 2-6 6-4 6-3 winner against David Nalbandian on Friday, will play Monaco on Sunday, while Llodra takes on Nalbandian in the final dead rubber.
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