A victory for the hosts never looked in doubt and they found themselves ahead within the opening five minutes as the talented David Alaba fired a free kick in from a central position, while Mario Mandzukic added a second with a header just before half-time.
Arjen Robben wrapped up the three points 22 minutes from time after a lovely assist by Alaba, thus securing a win in Pep Guardiola's first Champions League outing in charge of the German club.
Guardiola's men strolled to a similarly comfortable 2-0 win over Hannover at the weekend and the coach made only one change to that team as Dante replaced Daniel Van Buyten at centre-back.
The Russians also came into the game fresh from a domestic victory over Rostov, but the win came at a cost as Alan Dzagoev and Zoran Tosic both picked up injuries, meaning Aleksandrs Cauna and Steven Zuber took their respective places.
Bayern were in control from the start and they took the lead just four minutes in when Austrian Alaba steered a free kick past Igor Akinfeev from the edge of the box.
The hosts' dominance was obvious as they monopolised possession, but they struggled to break down CSKA's resolute defence.
When they did, 10 minutes from half-time, Mandzukic spurned a magnificent chance to double their lead. Rafinha crossed from the right and the forward headed the ball onto the far post before it rolled into the arms of Akinfeev.
But Mandzukic made amends three minutes before the break when Robben whipped in a fearsome free kick from the right and the Croatian forward diverted it past the helpless Akinfeev.
The visitors continued to struggle after the break and Robben could have scored a third, but his volley from inside the area was well saved.
Leonid Slutsky's men enjoyed a rare spell of possession in the hosts' half around the hour mark but they were almost punished soon after.
Mandzukic arrived in the box to meet Alaba's left-wing cross but again found Akinfeev in excellent form.
The Russian goalkeeper could do nothing to deny Bayern their third goal in the 68th minute, however.
Alaba produced a marvellous scooped pass over the CSKA defence and Robben smashed a low shot into the net.
Bayern continued to press for more in the dying stages as Robben's replacement Xherdan Shaqiri created danger on the right flank, but three goals were enough for Bayern who get their Group D campaign off to the perfect start.