In the opening matches for both, Wawrinka defeated Bernard Tomic 6-3, 7-6(6), while Ferrer easily dispatched of Alexandr Dolgopolov 6-2 6-2.
There were four first-round matches Tuesday: Roberto Bautista beat Pierre-Hugues Herbert 4-6, 6-3, 6-2; Viktor Troicki beat American Jack Sock 6-2, 6-3; Jeremy Chardy beat Lucas Pouille 3-6, 6-3, 6-2; and Edouard Roger-Vasselin beat Ivo Karlovic 4-6, 7-6(1), 7-6(5).
Wawrinka is trying to become the first player to win the French Open and the Paris Masters events in the same season since Andre Agassi in 1999. He faced five break points Tuesday, but saved them all, along with two set points against him in the second set.
"I wasn't in a good position, that's for sure, serving at 2-5," Wawrinka told reporters. "I played one good point, aggressive, and then (Tomic) missed easy forehand and I was back. I was just trying to stay with him... He's a way better player now. He's a more physical player, also. He's fighting way more. He has a better forehand and I think he has a better plan when he's playing."
Wawrinka will take on Feliciano Lopez or Viktor Troicki in the third round.
Meanwhile, Ferrer needed only an hour to defeat Dolgopolov and will face 12th-seeded Marin Cilic or Grigor Dimitrov in the next round.