Bayern's Dutch attacker Arjen Robben, Mario Goetze and Thomas Muller scored one apiece under the snow of the Khimki Arena, while Japanese playmaker Keisuke Honda was on target for CSKA.
The European champions, who bettered Barcelona's previous record set in 2002, arrived in the Russian capital already qualified for the knockout stages.
Maintaining their perfect record pushed them six points clear of second-placed Manchester City, who play Czech champions Viktoria Plzen later on Wednesday.
Robben, reflecting on Bayern's latest record, said: "We have often said that we don't play for these records, we play to win titles.
"But we have a great team and I'm proud to be part of it. It's a fantastic achievement to win 10 consecutive games in Europe, especially if you consider that we also played Barcelona and then Dortmund in the final on the way."
Bayern coach Pep Guardiola added: "It wasn't easy to play on the snow on an uneven and slippery pitch here but nevertheless we had a good match.
"We dominated play and produced quality football tonight." The German champions were missing several key players including Franck Ribery, Bastian Schweinsteiger and Mario Mandzukic.
CSKA were hit with a partial UEFA stadium ban due to the racist abuse of Manchester City's Yaya Toure in the Moscow club's previous Champions League match.
But the support of their fans, who filled the open sectors despite the freezing Moscow weather, inspired Russian champions CSKA to create a series of early chances mainly after four corners.
In the 17th minute Robben lifted the guests with a precise shot from 10 metres past helpless CSKA goalkeeper Igor Akinfeyev from Muller's pinpoint pass into the area.
After the break CSKA, who needed a point to secure their Europa League berth, moved up a gear and created several clear scoring opportunities for Honda.
Goetze increased Bayern's lead in the 56th minute when he received the ball 10 metres in front of the hosts' box and dribbled in despite the physical presence of five CSKA defenders to send the ball home from 10 metres.
In the 62nd minute Honda reduced the deficit from the spot after handball by Bayern's Brazilian back Dante in his area but three minutes later Muller restored the two-goal lead also with a penalty after Georgy Shchennikov fouled Robben in the box.
CSKA Serbian midfielder Zoran Tosic saw a late shot from the edge of the penalty box hit the woodwork. "Today we played a good match and looked adequate against the European champions," CSKA head coach Leonid Slutsky said.
"We created enough chances especially after the break but unfortunately showed an extremely poor percentage of conversion. "We are sorry about that but we have nobody to blame for the defeat except ourselves."