However, Bayern gradually seized the initiative and Mueller broke down the left flank to send in a cross for Robben who gave Igor Akinfeev no chance, hitting the back of the net with a left-foot shot from seven meters on the visitors' first scoring opportunity.
Honda created a chance for an equalizer one minute into first-time injury time, putting Ahmed Musa through on goal, only for Neuer to smother the Nigerian striker's poke.
The Japanese midfielder had two clear chances to equalize early in the second half but failed to beat Neuer in a one-on-one after latching on to Akinfeev's long kick and then missed again a minute later with the goal wide open following a cross from the right.
Goetze added Bayern's second after he rounded four CSKA players and curled the ball into the far corner of the net in the 65th minute.
CSKA, which 3-0 lost in Munich, finally scored but from the spot after a handball by Dante.
But there was soon a spot-kick at the other end after defender Georgy Schennikov fouled Robben in the box and Mueller beat Akinfeev with a low shot into the left corner.
The home side created several more chances but had no luck, with Tosic hitting the crossbar in the 78th.
"We had several clear scoring opportunities in the second half," CSKA coach Leonid Slutsky said. "But it was all about capitalizing. Unfortunately we failed to convert them. I'm really pleased with the way we played in the second half."
Bayern coach Pep Guardiola focused more on the conditions.
"It was a difficult game on a tough pitch and under a heavy snowfall," he said.
Bayern had equalled Barcelona's 2002-03 record of nine wins in a row three weeks ago
Bayern leads Group D with 15 points. CSKA has three points for third, six points behind second place Manchester City which has also reached the last 16 and was playing Viktoria Plzen later.
Bayern will next face Manchester City on Dec. 10, while CSKA will be on the road to Plzen to play for a spot in the Europa League.
