Three is certainly the magic number for Los Blancos, who have also failed to score in their last three matches and had a trio of efforts rebound off the post in Russia.
Julen Lopetegui was without a number of star players for the trip to Moscow, with Sergio Ramos, Gareth Bale and Marcelo all missing.
While FIFA Player of the Year Luka Modric was left on the bench as young defender Sergio Reguilon was handed his Champions League debut.
But things did not go to according to the book for Europe's current kings, who are looking to win the tournament for a fourth straight year.
Indeed, it was a man from Everton who scuppered Real's plans on a cold night in the Russian capital.
Nikola Vlasic was loaned to CSKA in the summer after failing to win over new boss Marco Silva.
But the 20-year-old Croatian needed just two minutes to put the hosts ahead.
A stunned Real attempted to mount a comeback as they dominated possession, although there was an injury blow as Dani Carvajal was forced off early on.
But even the introduction of Modric and new £30million striker Mariano, back at Real after impressing for Lyon, did little to improve Lopetegui's fortunes – although there was a late scare for CSKA when captain and goalkeeper Igor Akinfeev was sent off with minutes remaining.
Real are now yet to score in their last three games, having lost 3-0 to Sevilla before drawing 0-0 against Atletico.
And their shortcomings could force the board to make an emergency signing in January after they failed to replace talisman Cristiano Ronaldo.
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