Raonic served 15 aces and broke his French opponent three times to set up a match against Jarkko Nieminen, who thrashed Viktor Troicki 6-1, 6-2.
Bautista Agut was pushed a little harder, closing it out on his fifth match point when the 11th-seeded Frenchman netted a forehand. The Spaniard will next play Florian Mayer or Benjamin Balleret.
"I didn't produce anything during that first set. In fact, I was tired. Long rallies were killing me," Simon said. "In every game I was giving him a couple of free points, which hurts a lot on clay because from his side there were not many free points."
It was Simon's fourth straight defeat after losing to Tommy Haas in the Sony Open quarterfinals and both singles matches in France's Davis Cup quarterfinal loss to Argentina.
Fabio Fognini came from behind to down 15th-seeded Andreas Seppi 3-6, 6-4, 6-4 in an all-Italian match after converting seven of 10 breakpoint chances. He will next face Radek Stepanek or qualifier Albert Ramos.
Other first-round winners were Nikolay Davydenko, qualifier Pablo Andujar and Frenchmen Benoit Paire and Edouard Roger-Vasselin.
Davydenko beat qualifier Daniel Brands 6-3, 6-4; Andujar scraped past Jeremy Chardy 6-7 (4), 7-5, 6-2; Paire downed Ivan Dodig 6-4, 6-4; and Roger-Vasselin topped Robin Haase 6-3, 6-2.
Later, ninth-seeded Marin Cilic plays Horacio Zeballos.
Top-seeded Novak Djokovic will decide Tuesday whether he's recovered from his ankle problem to play Mikhail Youzhny or Daniel Gimeno-Traver on Wednesday. Also that day, No. 2 Andy Murray takes on Roger-Vasselin.