Leverkusen, who took the lead after 16 minutes through Kevin Volland, stay second Group E with seven points and will book their spot in the knockout rounds if Tottenham Hotspur lose to leaders Monaco later on Tuesday.
The Germans started brightly and were rewarded for their endeavour when Kevin Kampl played a delightful pass into Volland, who sprang the home side's offside trap and fired the ball past CSKA keeper Igor Akinfeev, who conceded for the 42nd consecutive game in the competition.
Defensive frailties have been the Russian champions' Achilles heel throughout their Champions League campaign this season and they almost surfaced again as Javier Hernandez had a goal ruled out for offside after CSKA were undone from a free kick.
CSKA pushed forward in the second half in search of an equaliser and levelled with 14 minutes remaining through Natcho's spot kick after Mario Fernandes was fouled in the area.
Both sides then had chances to grab a winner as Volland was denied by the woodwork after 80 minutes and Alan Dzagoev went close for the home side, who stay bottom of the group with three points with one match remaining.
(Reporting By Dmitriy Rogovitskiy; Editing by Toby Davis)
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