An efficient performance in front of goal ensured Bayern did not slip up in the snowy conditions as Arjen Robben, Mario Gotze and a Thomas Muller penalty did the damage as they beat Barcelona's previous record of wins set in 2002.
CSKA created enough chances to take something from the game, but only had a contentious Keisuke Honda penalty to show for their efforts as their bid to tie down a Europa League place was delayed.
The Russians spurned three presentable chances to open the scoring inside the opening 15 minutes.
Zoran Tosic and Sergei Ignashevich were both denied by defender Dante following Honda corners - the latter seeing his effort cleared off the line - and Bayern's shaky start continued when Pontus Wernbloom was allowed a header he only directed straight into the arms of Manuel Neuer.
CSKA's early hope was efficiently extinguished on 17 minutes by an incisive move for Bayern's opener.
Toni Kroos won the ball high up the pitch and threaded a pass for Thomas Muller on the left flank. Muller had time to wait for Robben to make ground into the area and supply a perfectly-weighted pull-back that the winger smashed past Igor Akinfeev despite the goalkeeper being well positioned.
Bayern's class then started to show as Gotze showed off a couple of stepovers before chipping a pass that was just over Muller as he got between the defensive line and goalkeeper.
Bayern suffered an injury setback on the half-hour when Phillipp Lahm appeared to pull up with a leg injury and was replaced by Thiago Alcantara to make his Champions League debut for the Bavarians.
CSKA were struggling to get a share of the ball but should have been level when Musa missed a golden chance in first-half injury-time.
Honda's clever flick foxed Dante and left Musa with only Neuer to beat. He panicked, though, before fluffing a shot that harmlessly rolled for Neuer to pick up.
If that was CSKA's best chance of the first half, Honda spurned an even better opportunity seconds after the restart.
Akinfeev's long punt caught out Jerome Boateng and Honda ran into acres of space. The midfielder appeared to have too much time, however, as he pondered his options before Neuer stole the ball off his feet.
CSKA were punished in full by another moment of Bayern class on 56 minutes.
Gotze's quick feet allowed him to escape as four defenders closed in before arrowing his shot into the corner.
At 2-0 down CSKA needed some inspiration and were handed it by a contentious penalty decision.
Dante was whistled for handball after a shot crashed against his arm at close quarters, and after the defender was booked for his protests, Honda sent Neuer the wrong way.
It took Bayern three minutes to respond to the danger as they won a penalty of their own.
A Gotze shot hit the post and when Georgi Shchennikov took too long to clear the rebound, Robben nipped in and attracted a foul. Muller tucked away a carbon copy of Honda's penalty moments earlier.
CSKA kept up their pressure and Tosic rattled the crossbar with 12 minutes left, but Robben could have made the score even more emphatic but for an Akinfeev save.