The visitors recovered from their shock loss to BATE Borisov a fortnight 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 truth be told, Jupp Heynckes' side should have been goal up within a minute of the kick-off.
Philipp Lahm picked out Thomas Muller pefectly with a right-wing cross, but the Germany intenrational'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.
Thereafter, the Bavarians began to take control, and Franck Ribery was looking lively, forcing untried youngster Djibril Sidibe into a string of clumsy fouls, only for Bayern's set piece taker to fail to deliver.
And, they almost paid for it. Despite Lucas Digne frequently allowing Muller and Lahm too much room on the wings, he was excellent going forward, and on one dart down the left, he found Tulio De Melo, who could only head wide under pressure from Dante.
Soon enough, though, Bayern's dominance paid off. Lahm took advantage of a drop in concentration from Digne, darted into the box, and fell, slightly softly, under a challenge from the full-back. Muller stepped up, and calmly passed the ball into the back of the net from the spot.
The match then continued in much the same manner that it had been previously. Bayern were almost unchallenged in possession, stroking the ball around harmlessly in the centre of the park without any real penetration.
Digne, eager to make up for his mistake in giving away the penalty made another charge down the wing and sent in a fantastic cross that narrowly evaded the heads of Nolan Roux and De Melo, before Marvin Martin screwed a long-range volley wide from distance with Manuel Neuer out of position.
However, all things told, Lille did not do enough to warrant an equaliser before the break, allowing Bayern to take their slender lead into the break, despite a meagre performance.
After the restart, the hosts returned with more vigour, pressing Bayern more in midfield, but spare a pop shot from Florent Balmont which was blocked by Dante's head, they were no closer to grabbing an equaliser.
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 Lille defence, who eventually managed to clear their lines with Mario Mandzukic lurking.
Shaqiri then had credible appeals for a penalty turned down after a left-wing cross struck Franck Beria on the arm from close range, while Bastian Schweinsteiger failed to play in Lahm, who had won the ball brilliantly just outside the box and attempted a give-and-go with his team-mate.
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.
And, within seconds, they were almost made to pay for their error. Ryan Mendes, fresh from the bench, was gifted possession by Dante inside the Bayern box, but saw his effort blocked by Schweinsteiger.
He recovered the ball and dinked in a cross, but Lahm stood firm and stopped his attacker from getting control.
Perhaps rattled by the Lille resurgence, Heynckes brought Luiz Gustavo on for Kroos, and although the hosts continued to press, Bayern had done just about enough.
Lille now sit six points behind all their fellow Group F sides. Heynckes' side, meanwhile, can take a huge step towards progression when they host les Dogues in a fortnight's time.