The hosts threatened sporadically on the break, but Müller's strike from the penalty spot after 22 minutes always looked like it would be enough to earn maximum points for Pep Guardiola's side.
Götze the threat
In front of an eerily quiet stadium, with the game played behind closed doors as a punishment for crowd misbehaviour during the Russians' clash with FC Viktoria Plzen last December, FC Bayern were dominant from the outset. Arjen Robben drew a sharp save from Igor Akinfeev on ten minutes, while Mario Götze looked a constant threat. And it was Götze's attacking play that lead to the first goal: he skipped into the area and was brought down by Mario Fernandes for a penalty, which Müller despatched with ease.
Ahmed Musa gave the German champions a scare late in the half, using his pace to get beyond Medhi Benatia and bear down on Manuel Neuer's goal, but the Germany No1 was equal to his effort. Roman Eremenko also fired narrowly over, before Robert Lewandowski and Götze almost scrambled a second.
Early second half scare survived
Buoyed by their strong end to the first half, the hosts continued to look dangerous straight after the break. Musa once again carried the most threat, but he was unable to get a shot away after another quick counter. Nevertheless, Bayern continued to enjoy the lion's share of possession and CSKA's defence had to be constantly alert to the array of runners coming their way.
As the game wore on, the Russian side tired and Bayern were presented with a few more openings. Benatia played in Müller, but his attempt to poke the ball around the onrushing Akinfeev into the path of substitute Xherdan Shaqiri was intercepted and cleared for a corner. Shaqiri did get the ball in a dangerous position from Lahm's cute dink moments later, but again Akinfeev was out quickly to smother. Fortunately for the 2013 winners a second goal wasn't needed and Bayern kept their 100% record in this season's Champions League.
CSKA: Akinfeev - Mario Fernandes, V. Berezutskiy, Ignashevich, Shchennikov - Natcho (Doumbia 66'), A. Berezutskiy - Tosic (Efremov 78'), R. Eremenko, G. Milanov - Musa
FC Bayern München: Neuer - Benatia, Dante, Alaba - Lahm, Xabi Alonso, Juan Bernat - Robben (Rafinha 81'), M. Götze (Shaqiri 77') - T. Müller - Lewandowski (Pizarro 90')
Goals: 1-0 (Müller 22', pen)