Lacina Traore put the 'Army Men' in front against his parent club in the 34th minute but Bernardo Silva grabbed the equaliser late on.
CSKA were desperately disappointing three weeks ago against Tottenham Hotspur but the Russians found top gear straight away against Monaco, causing problems with their pace and direct approach.
The impressive Alexander Golovin orchestrated play from midfield and the hosts took the lead after 34 minutes following a good team move.
Zoran Tosic curled in a left-foot shot that Danijel Subasic could only parry and Traore tapped the rebound into an empty net.
Igor Akinfeev then produced a stunning reaction save from close range at the other end to deny Andrea Raggi a goal.
Monaco put CSKA under considerable pressure early in the second half and captain Valere Germain went close when his effort was thwarted by a last-ditch challenge from defender Vasili Berezutski.
Akinfeev made another top-class stop to deny Benjamin Mendy and the Russian international looked destined to keep his first clean sheet in the group stages at the 40th attempt.
However, Silva levelled for the visitors with three minutes remaining.
Monaco have five points from three games, one in front of Tottenham. Bayer Leverkusen are on three points while CSKA have two.
(Editing by Tony Jimenez)
