The visitors recovered from their shock loss to BATE Borisov two weeks ago and grabbed their second European victory of the season against the tame Dogues.
The Bavarians were in control for much of the match without ever really getting out of first gear, and Thomas Muller's 19th-minute penalty proved to be enough on the night. The hosts looked vulnerable from the outset, and Jupp Heynckes' side should have been goal up within a minute of the opening kick.
Philipp Lahm picked out Muller pefectly with a right-wing cross, but the German international's control failed him when he was completely unmarked. Had he taken a more measured first touch, he would have surely found the target from a matter of yards.
The Bavarians maintained control, and Franck Ribery, who came through Lille's youth academy, was looking lively, forcing untried youngster Djibril Sidibe into a string of clumsy fouls, only for Bayern's set piece takes to fail to deliver.
Soon enough, though, Bayern's dominance paid off. Lahm took advantage of a drop in concentration from Lucas Digne, darted into the box, and fell, slightly softly, under a challenge from the fullback. Muller stepped up, and calmly passed the ball into the back of the net from the spot to break the deadlock.
After the halftime restart, the hosts returned with more vigor, pressing Bayern more in midfield, but spare a pop shot from Florent Balmont that was blocked by Dante's head, they were no closer to grabbing an equalizer.
At the other end, an excellent block from Sidibe forced Xherdan Shaqiri's volley well over the bar, while a Muller cross caused mayhem among the static LOSC defense, which eventually managed to clear its lines with Mario Mandzukic lurking.
Muller missed a golden opportunity to kill off the game 14 minutes from time, trying to sweep home a Lahm cross with his right foot when he could have had a tap in with his left. Within seconds, he was almost made to pay for his error. Ryan Mendes, fresh from the bench, was gifted possession by Dante inside the Bayern box, but saw his effort blocked by Schweinsteiger.
Lille now sits six points behind all other Group F sides. Bayern Munich, meanwhile, can take a huge step towards progression when its host Les Dogues in two weeks.