The man who contributed to the opening strike, Kroos, aimed to make amends for his earlier error with a deflected shot that forced Igor Akinfeev to push away for a corner.
A lovely chance for CSKA to add a second went astray after Vlasic exchanged passes with Fedor Chalov who fired into the legs of Nacho Hernandez for a corner.
From the corner, Nikita Chernov managed to get underneath the ball only to head over the top on 17 minutes.
The chances continued falling for the home side after a rebound inside the box was met by Fedor Chalov who forced Keylor Navas to get down low to make a save four minutes later.
The closest Madrid came to levelling found Casemiro attempting to slide the ball into the bottom corner after being allowed the time to run with the ball.
Akinfeev was eager to prove his worth once more after doing so at the summer’s World Cup, with a save off a shot from Nacho Fernandez on 37 minutes.
Frenchman Karim Benzema managed to send a curling shot right over the crossbar after being allowed to get away from his marker within minutes.
Madrid stepped up just before halftime as Benzema struck the crossbar after rising to meet a cross with his head.
An injury blow affected Real as Dani Carvajal hobbled off on the stroke of halftime. Adrian Odriozola took his spot.
Five minutes from the break, Marco Asensio took a 20-yard shot cleanly but it was well saved in the end by Akinfeev.
Eight minutes later, Madrid made a double change. Luka Modric who played at this venue in the World Cup final entered and so did Mariano Diaz.
CSKA first change happened on the 66 minutes after Alan Dzagoev who had seen little of the ball made way for Dmitri Efremov.
Kroos fired in a shot form 22-yards out as Los Blancos continued pressing for the elusive equaliser in the final minutes.
After coming from the bench to curl home against AS Roma, Diaz watched the ball drop over his shoulder before volleying wide of target on 83 minutes.
In the opening minute of added time, Diaz became the third Real player to be denied by the frame of the goal after seeing his header struck the left post just moments before Akinfeev was sent off for a second bookable offence.
The result throws the group wide open, while it’s a famous win for Moscow who get their campaign underway in fine style.