The Colombia striker struck his 41st and 42nd goals from 46 matches in UEFA club competitions in the first half after Valere Germain's opener to put the Ligue 1 team on eight points from four games.
Bayer Leverkusen are second in Group E after claiming a 1-0 win at Tottenham Hotspur, who are third on four points with CSKA in bottom place with two points.
CSKA next host Leverkusen while Monaco will take on Tottenham on Nov. 22.
Leo Jardim's side got off to a confident start and Germain, collecting a poor clearance, dribbled past Igor Akinfeev and pushed the ball into the empty net in the 13th minute.
Falcao doubled the tally in the 29th minute by latching on to fullback Benjamin Mendy's cross from the left and beat the Russian keeper from close range.
The Colombian was at it again four minutes before the interval, stabbing the ball past Akinfeev after being picked out by Germain in the area.
Second-half substitute Guido Carrillo came close to adding a fourth two minutes from time but his strike hit the post.
(Writing by Julien Pretot, editing by Pritha Sarkar)
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