In-form Bayern breeze past Villarreal
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."
Bayern quickly took command at the Madrigal with Franck Ribery in particular causing havoc in the home defence.
The French international dribbled down the left flank and pulled back for Kroos to side-foot a shot inside the far post.
Villarreal tried to react but only had a couple of glimpses of goal before the break which Giuseppe Rossi and Mario Gaspar failed to put away.
They lifted their game for a while in the second half, but as a side accustomed to dominating possession, they laboured as Bayern refused to relinquish the ball.
Home keeper Diego Lopez was the busier and Kroos should have killed off the game for the Germans earlier when he fired against the post from close range in the 69th minute.
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."