A 22nd-minute Thomas Mueller penalty put them in the driving seat but despite a string of chances they just could not add to their score.
New transfer Robert Lewandowski, who has so far scored only one goal in a competitive game after clinching the Bundesliga top scorer title last season, had another disappointing night, failing to threaten.
Chances by Mueller, Mario Goetze and Arjen Robben were also wasted as the Bavarians, who were made to work hard against a crowded Russian defence, struggled to make their supremacy count.
"Not only because of the absent fans but also the way CSKA played it was a strange game," Mueller told reporters.
CSKA were forced to play behind closed doors following punishment for racist behaviour of fans.
"It was not easy for us and our lead did do us a lot of good. But we could and should have scored more goals and CSKA were constantly dangerous on the break," Mueller added.
Despite fielding a team who included attacking players like Lewandowski, Goetze, Mueller and Robben, Bayern could not convert any more of their chances in a largely one-sided encounter.
With first-choice central defender Jerome Boateng languishing on the bench with a minor injury and replacement Mehdi Benatia repeatedly outclassed by the Russians, Bayern allowed CSKA to continue hoping for an equaliser until the very end.
Roman Eremenko rattled the cross bar and Bayern keeper Manuel Neuer twice came to the rescue in one-on-one situations to protect their lead.
For coach Pep Guardiola, however, who has repeatedly said his team needed more time to peak due to World Cup fatigue and injuries, the three points that put them top of Group E were all that mattered.
"We can be satisfied to have gotten the three points," said the Spaniard, who led Bayern to the domestic double in his first season in charge. "But up front we were a bit sloppy with the chances because otherwise we were in control."
Guardiola was more affected by the empty tribunes.
"I have been involved in football for 40 years now and I have never seen anything like it. I hope I never have to experience this again."
(Editing by Julien Pretot)
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