The German scored a Lionel Messi-esque effort, as well as strikes from Arjen Robben and Thomas Muller, for the club's 10th consecutive European triumph.
Arjen Robben's 10th goal of the season set the European champion on its way as the snow came down in the Russian capital and Mario Gotze doubled the lead early in the second half.
Keisuke Honda pulled a goal back from the penalty spot after spurning two golden opportunities after the break, but Thomas Muller responded with a spot kick at the other end to ensure Bayern surpassed the record of nine Champions League victories in a row set by Barca in 2002-03.
Pep Guardiola's side will be confirmed as Group D winner if Manchester City fails to beat Viktoria Plzen later on Wednesday but, even if the Premier League side claims all three points, the German champion will only need a point against Manuel Pellegrini's side next month to ensure it claims top spot.
Victory also marks a club record sixth consecutive away win in Europe for Bayern, while CSKA is still in the hunt for a place in the Europa League ahead of its final game against Plzen.
Bayern striker Mario Mandzukic was ruled out with a calf problem, so Gotze started in attack. CSKA was without in-form striker Seydou Doumbia due to injury and Ahmed Musa came in to replace him.
Guardiola warned his players to adapt quickly to the weather conditions and Bayern did just that to edge in front after 16 minutes.
Muller was the architect, racing away down the left and cutting the ball back into the path of the onrushing Robben, who beat Igor Akinfeev with a clinical left-foot finish inside the near post.
Honda tried to be too clever when he attempted to round Manuel Neuer two minutes into the second half, but the German goalkeeper read his drag back and smothered the ball.
Things went from bad to worse for the Japan international when a cross from the right fell nicely for him six yards out, but he fluffed his lines with the goal gaping.
He was made to pay for those misses 11 minutes into the second half, when Gotze set off on a mazy run into the penalty area and beat Akinfeev with a delightful left-foot finish.
CSKA was given a life line five minutes later, when Dante was harshly adjudged to have handled in the area and Honda this time kept his nerve to send Neuer the wrong way from the spot.
However, Bayern was awarded a spot kick of its own after 65 minutes when Georgi Schennikov upended Robben and Muller restored the two-goal advantage. Zoran Tosic hit the crossbar nine minutes from time, but Bayern never looked in danger of surrendering the lead.