U.S. Open champion Samantha Stosur, the runner-up here two years ago, raced to a 5-0 lead before beating American world number 112 Irina Falconi 6-1 6-4.
"I thought it was a good, solid match," the Australian sixth seed said. "I was happy with the winners that I hit. I thought you could always hit a few less errors... Overall, I'm quite happy with it."
Argentine men's ninth seed Juan Martin del Potro also reached the third round with a 6-7 7-6 6-4 victory over Frenchman Edouard Roger-Vasselin and will now play Croatian Marin Cilic.
"It's going to be tough," Del Potro told a news conference. "We know one another well, very well. The matches we play are always very difficult matches. The way he plays tennis is similar to my way of playing tennis."
After the shock first-round defeat of pre-tournament favourite Serena Williams on Tuesday, sister Venus was due on Philippe Chatrier court in the last match of Wednesday, playing third seed Agnieszka Radwanska of Poland.
Venus, a seven-times grand-slam winner and former world number one, has been rebuilding her life and game after being diagnosed with an autoimmune illness.
In Image: Australia's Samantha Stosur waves after defeating Irina Falconi