The Group E match was played in front of an empty house after a ban from European soccer's governing body UEFA was imposed for the racist behaviour of CSKA's fans.
The lack of atmosphere only made life more comfortable for the five-time champions as they dominated proceedings on the way to their second straight victory in this year's competition.
The German champions could have scored several against the injury-hit hosts but CSKA put up a spirited performance and could look back with dismay on their own missed opportunities.
CSKA's Finland midfielder Roman Eremenko even hit the bar in the first half with one curling effort but the decisive moment proved to be Mueller's 21st minute spot-kick.
After Germany team mate Mario Goetze was fouled in the area by Mario Fernandes, Mueller notched his 22nd career goal in Europe's elite competition with his expertly-taken strike. Goalkeeper Igor Akinfeev had conceded in his last 22 Champions League matches, dating back to 2006, and his unwanted record continued as he picked the ball gloomily out of the net.
BLAZED OVER
Goetze could have put the Bundesliga leaders ahead after nine minutes but Germany's World Cup final match-winner blazed a right-footed effort over the bar from close range.
When CSKA slowly began to find their rhythm, the quick feet of Ahmed Musa caused problems for the visitors' defence. The diminutive Nigerian forward managed to get free of Bayern's Mehdi Benatia and home in on goal but was foiled by Manuel Neuer's excellent save. The ball broke kindly for Zoran Tosic, who had time and space to manoeuvre the ball on to his favoured left foot, but the Serbian international ballooned the ball over the bar from an excellent position. CSKA were left to rue a number of missed chances in the first half but Bayern shut down the game expertly after the break, controlling the threat of CSKA substitute Seydou Doumbia and hardly giving the hosts a sniff of an equaliser.
It was Bayern who came closest to scoring again, with Goetze curling an effort just wide, but manager Pep Guardiola could at least be satisfied to see his side leading Group E with a maximum six points before AS Roma sought to match them with a victory at Manchester City in one of Tuesday's later games.
CSKA have still to earn a point but their performance was a vast improvement on their 5-1 trouncing in Rome a fortnight earlier.
(Reporting By Dmitriy Rogovitskiy; Editing by Ian Chadband)
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