Thomas Muller's first-half penalty and late goals from Sebastian Rode and Mario Gotze sealed a routine victory for Bayern, while defeat for CSKA means they cannot even enjoy the consolation of Europa League football in the new year.
The Bundesliga champions came into Wednesday's clash at the Allianz Arena already confirmed as pool winners, while the picture was slightly more complicated for CSKA.
Leonid Slutsky's men needed a win in Munich and had to hope the game between Roma and Manchester City in Italy ended in anything other than victory for the home side.
In the end, City claimed second spot with a 2-0 win in Rome while CSKA finished bottom of the group with five points.
The most pleasing aspect of a straightforward dead-rubber win for Bayern boss Pep Guardiola is sure to be the long-awaited return to his starting XI of Germany captain Bastian Schweinsteiger, who began a match for the first time since the World Cup final in July.
Guardiola made five alterations from Bayern's 1-0 win over Bayer Leverkusen at the weekend, including bringing in Schweinsteiger and 18-year-old midfielder Gianluca Gaudino for his Champions League debut.
Seydou Doumbia, recalled as one of three CSKA changes from the 1-0 victory at Kuban Krasnodar on Saturday, flashed an early header off target but it was the home side who took the lead in the 18th minute.
Bebras Natcho felled Franck Ribery inside the area, and Muller coolly converted the resulting spot-kick to become Bayern's leading goalscorer in this competition with 24.
Doumbia almost produced a sensational equaliser five minutes later when he found himself one-on-one with Manuel Neuer after a mazy run, but his finish was weak and stopped by the legs of the goalkeeper.
That chance apart, Bayern continued to dominate possession and went close to a second shortly before the break when Schweinsteiger saw his shot tipped over by Igor Akinfeev.
Guardiola replaced Muller and Ribery with Robert Lewandowski and Arjen Robben at half-time, and the latter threatened with a thumping drive straight at Akinfeev just before the hour.
Ahmed Musa fired wide when off-balance in a rare CSKA attack 10 minutes later, but Akinfeev was again called into action to stop Robben from close range shortly after.
Lewandowski again went close 10 minutes from time, seeing his initial effort blocked by Akinfeev before rolling the rebound against the base of the post and seeing Mario Fernandes hack clear off the line.
A second goal did arrive four minutes later, though, as Schweinsteiger stood up a cross from the left and Rode was left all alone to head in from close range at the back post.
And Bayern added gloss to the scoreline when Gotze applied a simple finish following neat interplay on the edge of the area in the 90th minute.
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