The result, coupled with Valencia's 3-0 win away to BATE Borisov, leaves Bayern and the latter two teams neck-and-neck on six points apiece, with Lille stranded at the bottom of the group, still waiting to get off the mark.
Chances were at a premium in a tightly-contested opening 45 minutes, with Bayern dominating possession but needing Müller's penalty to edge in front. After the restart, the match was more evenly-balanced and the visitors ended up counting down the minutes as Lille pressed in vain for the leveller.
Bayern in control
Jupp Heynckes made only one change to his starting eleven following Satturday's impressive 5-0 against Fortuna Düsseldorf, which sealed Bayern a record-breaking Bundesliga start of eight straight wins, selecting Javi Martinez in place of Luiz Gustavo in one of the holding midfield slots.
Bayern looked very much in control in the opening period, but failed to benefit from their lion's share of possession against the deep-lying hosts, with only Müller getting anywhere near goal just after kick-off when the Germany international couldn't control Philipp Lahm's long ball.
However, the visitors' pressure took its toll 20 minutes into the game when Lahm dashed into the box and was fouled by Lille's left back Lucas Diagne, who left English referee Martin Atkinson no alternative but pointing on the spot, with Müller coolly slotting the subsequent penalty into the low right corner.
Ribery off at half time
Lille, whose numerous fouls seemed to interrupt Bayern's flow, throughout the first half longed for opportunities to beat the 21-times Bundesliga champions on the break, which resulted in two half-chances before half-time, but Tulin de Melo clearly missed the near left post with his header while Marvin Martin's volleyed the ball far.
Both teams resumed in similar style after the interval, with Bayern dominating despite Franck Ribery being substituted at half-time due to injury on the French international's return to the cub he played for at youth level, yet lacking ideas in the last third of the pitch.
However, the match opened up after an hour, when Xherdan Shaqiri, who came in for Ribery, had his attempt from the edge of the box cleared at the expense of a corner and Toni Kroos's volley went over the crossbar while, on the other side of the pitch, Lille's long-range attempts by captain Florent Balmont after 68 minutes and Dimitri Payet (70') went wide. Müller should have done better 13 minutes from time, but accidentally kneed Lahm's cross from the right past the target.
Despite Bayern's defence not always appearing solid in the final stages, France's 2011 champions were unable to seriously threaten Manuel Neuer's goal as the game went into its final phase and Bayern duly saw the win through. The two teams will lock horns again in the return fixture at the Allianz Arena in a fortnight's time.
LOSC Lille: Landreau - Sidibé, Beria, Chedjou, Digne - Pedretti (90. Rozehnal) - Balmont, Martin - Kalou (56. Payet), Tulio de Melo, Roux (78. Mendes da Graca)
FC Bayern Munich: Neuer - Lahm, Boateng, Dante, Badstuber - Schweinsteiger, Javi Martinez - T. Müller (84. Alaba), Kroos (81. Luiz Gustavo), Ribery (46. Shaqiri) - Mandzukic