Lille full-back Lucas Digne fouled Philipp Lahm and Mueller converted from the spot after 20 minutes.
Bayern, stunned by Belarus's BATE Borisov in their last game, were in complete control throughout and Lille, who have never beaten a German team, did little to threaten Manuel Neuer's goal.
"Tonight we showed that we have a very experienced team," Bayern coach Jupp Heynckes told reporters.
"There were few chances and I can congratulate my team who fought to win this game. When you only have a one-goal edge, anything can happen. But I have to give a lot of credit to our defense."
Bayern, BATE and Valencia all have six points from three matches with Lille yet to claim a point.
Frenchman Franck Ribery tormented Lille, and in particular his marker Djibril Sidibe, in the opening 45 minutes but suffered at the hands of some rough challenges and did not appear after the break because of a muscle pain.
Winger Ribery was rejected as a teenager by the northern French club, who released him after four years in their academy for what they called "bad behaviour".
Despite some solid recent displays for France, setting up Olivier Giroud's last-gasp equaliser in Spain in the 2014 World Cup qualifier two weeks ago, Ribery was booed each time he touched the ball.
Lille have now won only one of their last 11 Champions League games and have not registered a victory at home in their last seven.
"We clearly do not have the size for this competition," Lille's coach Rudi Garcia said.
"I can only congratulate my players for having challenged Munich tonight. I just regret that Bayern were helped, they did not need it," he added, referring to the penalty.
Lille did not have the craft to test Bayern. Tulio De Melo headed wide from Digne's cross in the first half and their attempts on goal after the break were restricted to long-range efforts.
Salomon Kalou, part of the Chelsea side that defeated Bayern in the Champions League final in May before joining the French side last summer, disappointed again and was replaced after an hour.
