The result lifted CSKA to joint second spot in the first division with 33 points from 17 games, level with Spartak and Lokomotiv Moscow, who host neighbours Dynamo on Sunday.
The chasing trio are three points behind leaders Zenit St Petersburg, who lost 2-0 at home to Rostov on Friday after their 4-2 defeat at Spartak before the international break.
Saturday's pulsating derby was settled in the eighth minute when Doumbia capitalised on a defensive mix-up between keeper Artyom Rebrov and defender Yevgeni Makeyev, stroking the ball into an empty net after the two Spartak players collided.
Chances in a high-tempo clash came thick and fast at both ends, with one of the best falling to Spartak's Denis Glushakov who almost equalised when his scorching shot was cleared off the line by CSKA's Brazilian defender Mario Fernandes.
(Writing by Zoran Milosavljevic; editing by Josh Reich)
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