The meeting, which took place in Moscow at the Otkritie Arena, ended with a score of 1: 0 in favor of the home team.
CSKA remained with ten men in the 37th minute - Ilzat Akhmetov received a direct red card.
The victory for Spartak was brought by the goal of Jordan Larsson, who distinguished himself in the 52nd minute.
"Spartak" with 50 points takes the third place in the RPL standings.
CSKA is sixth with 46 points.
Earlier it was reported that the referee Igor Fedotov called Akhmetov's removal in the Spartak-CSKA match erroneous.