Toni Kroos put them ahead after only seven minutes and the European heavyweights, making their 250th European Cup appearance, dominated for the rest of the match.
Substitute Rafinha sealed the result with a wonderful piece of skill to create and score the second goal in the 76th.
It was Bayern's seventh consecutive victory in all competitions, with 21 scored and none conceded, and they moved straight to the top of the group with Manchester City drawing 1-1 at home to Napoli.
"I am pleased because this team has proved it can compete in Europe," Bayern coach Jupp Heynckes told reporters.
"It's a difficult stadium and winning has given us confidence for the coming games. It was a first half where we managed to gain an advantage, and a second where we dominated more comfortably."
Rafinha, a first half substitute for the injured Daniel van Buyten, ended Villarreal's hopes when he dribbled off the right, nutmegged his marker and smashed the ball past a surprised Lopez at his near post.
"The first goal, after only seven minutes, conditioned the rest of the match physically, tactically and psychologically," Villarreal coach Juan Carlos Garrido said.
"In the Champions League you play against the best in the world. We need to draw conclusions and try and improve."
