The victory put CSKA level with the Turkish side on four points, two behind Inter Milan, 1-0 winners at Lille.
Ivory Coast striker Doumbia put the Russians ahead in the 29th minute after being set-up by Vagner Love's clever back-heel.
Doumbia, who scored CSKA's goals in a 2-2 draw at Lille in their group opener last month, completed the rout with a great solo effort four minutes from time.
"Trabzonspor are a good team with good players and their win over Inter Milan did not surprise me at all," Doumbia told reporters.
"But tonight we were the better team because we created a lot of chances and scored three goals and also kept our concentration from the first minute to the last."
"I think we fully deserved our victory tonight," CSKA coach Leonid Slutsky told Russian television NTV Plus.
"We controlled the tempo and created most of the chances in the game while they only had one clear chance in the first half.
"I'm especially pleased because we did not give up a goal in a Champions League match for the first time since holding Arsenal [to a 0-0 draw in London five years ago]."
"We didn't win but it's not the end of the world. We still have three more games to play," said the Trabzonspor coach.
