The defeat all but ends winless Lille's challenge in the competition.
It was a far from polished performance but the result restored confidence to a Bayern side who had lost to BATE Borisov last time out.
The win leaves Jupp Heynckes' men locked on six points alongside Valencia and BATE, with only the top two advancing to the knockout stage.
Bayern admitted before tonight's match they were feeling the pressure slightly following a surprise 3-1 defeat in Belarus last time out.
But they settled quickly at Stade Metropole and had the first chance after 13 minutes, with Toni Kroos' free-kick punched away by goalkeeper Mickael Landreau.
Lille launched an immediate counter-attack and could have scored themselves but Tulio De Melo headed a cross from Lucas Digne past the left post.
Digne then fell out of favour with the home supporters after 20 minutes when his challenge in the area on Philip Lahm saw Bayern awarded a penalty.
Muller took responsibility for the spot-kick and slotted home low to give the Bundesliga side the edge.
Lille were desperately hoping for a good performance having conceded five goals in their opening two group matches, but were struggling to make an impression on their German opponents.
And the best they could produce before the break was a long-range drive from Marvin Martin which flew wide of the right post.
There were signs of improvement from the Ligue 1 club at the start of the second half when a powerful effort from Florent Balmont was blocked on the line by Bayern defender Dante.
Nolan Roux followed that chance up with a right-footed drive which cleared the crossbar of visiting goalkeeper Manuel Neuer.
Lille's defence soon found themselves under pressure again and De Melo almost gifted their opponents a second goal on the hour mark when his botched clearance was volleyed narrowly over by Kroos.
However, the French hosts were pushing forward more themselves, although both Balmont and Dimitri Payet wasted openings by blasting over.
Muller could have added his name to the scoresheet again 13 minutes from time but turned Lahm's perfect centre past the post from 10 yards.
Lille continued to put in the effort until the final whistle but Digne's stoppage-time strike - which was high and wide - summed up their frustration.