David Alaba, Mario Mandzukic and Arjen Robben were on target for Bayern, who have now won their last 10 opening Champions League fixtures.
Bayern got off the mark near enough straight away in this Group D fixture as Alaba handed them the lead in the third minute.
The 21-year-old midfielder was brought down by Pontus Wernbloom 25 yards out and punished him with a vicious free-kick that beat goalkeeper Igor Akinfeev.
Alaba could have doubled the lead for Pep Guadiola's side minutes later with his cross heading into dangerous territory before Vasili Berezutsky cleared the ball to safety for the visitors.
Mandzukic was next to have a go at the CSKA goal and he took on Akinfeev with a close-range shot, but the goalkeeper managed to get his feet to the ball to deny a second goal.
The visitors took a while to settle in before Ahmed Musa came close to netting an equaliser, his long-range effort sailing past the right-hand goalpost.
Down at the other end, Alaba almost turned provider as he set up Mandzukic with a cross into the penalty box, but the Croatia international's header went just over.
Bayern were dominating and Marcio Rafinha could have added a second as he fired inches wide from the edge of the area.
Franck Ribery then forced a block from Kirill Nababkin before Arjen Robben's close-range effort was just off target.
Leonid Slutsky's visitors were fighting to get into the match and Santos Vitinho came close to dragging the score back level but his drilled strike from 20 yards out was caught by Manuel Neuer.
Robben had another attempt at goal denied before he set up Mandzukic with a cross into the box, but the 27-year-old striker's header hit the post.
But Bayern's dominance paid off as they doubled the lead minutes before the break, again the result of a free-kick.
Rafinha was brought down by Vitinho and Robben's cross picked out Mandzukicto head home.
Slutsky made a tactical move at the start of the second half, bringing on midfielder Zoran Tosic for striker Vitinho as the away side attempted to wrestle their way back in.
Robben was unlucky not to get on the scoresheet minutes later as Akinfeev kept out his goalbound effort, then down at the other end Philip Lahm blocked Steven Zuber's shot as CSKA sought a way back.
Robben eventually made it three after a dominant second-half spell from the German side.
The Holland international collected Alaba's pass on the right before drilling the ball into the bottom right of the CSKA goal to show the rest of Europe they are serious about defending their title.
Ribery set up Mandzukic as Bayern went looking for a fourth but Akinfeev caught his close-range header.
And substitute Xherdan Shaqiri may have scored a fourth as he had a shot on goal after picking up Thomas Muller's free-kick, but his weak effort was comfortably collected by Akinfeev.
At the other end, Georgi Milanov's strike sailed over the bar to deny the away side a consolation.