Top-seeded Monfils and No. 2 Ferrer have yet to drop a set through two rounds.
Monfils beat fellow Frenchman Josselin Ouanna 6-4, 7-5, managing to hit 12 aces and convert three of 16 break chances.
"Josselin and I are the best of friends, so it's quite hard to play against him," Monfils said. "We've played each other maybe 10 times in tournaments, but this was the first time in a ATP World Tour event. Hopefully one day we'll fight it out in a (Grand) Slam too. He served well today and gave me a real fight."
Ferrer, aiming to surpass his semifinal run last year, beat Swedish qualifier Filip Prpic 6-3, 6-4, though he expressed disappointment afterward.
"I was frustrated with the way I was playing, and I served badly in the second set," said Ferrer, who smashed his racket in anger at one point. "But to get through the match just before the rain came down was a relief. Prpic is a good player and a tough guy to beat, and I had to fight hard out there."
The only other player to beat the afternoon rain was India's Somdev Devvarman, who reached his third career quarterfinals in beating Brazil's Thiago Alves 6-4, 6-1.
Alves struggled with the heat and had to call for a medical timeout at one point.
"I did feel for him," Devvarman said. "Although he started well by ripping some winners past me, he started to look sluggish as the game progressed. But I was very happy with my own game."
Seventh-seeded Yen-hsun Lu of Taiwan made it to his first quarterfinals in almost two years when he defeated South African wild card Raven Klaasen 6-4, 7-5 in just under two hours. Lu plays Monfils next.