The Ivorian scored his third goal in as many Champions League matches after Vagner Love coolly back-heeled the ball into his path in the 29th minute.
Aleksandrs Cauna added the second with a left-footed volley before Doumbia sealed the win four minutes before the final whistle with some great skill at the edge of the area to beat two defenders and find the back of Tolga Zengin's net.
The win was a much needed boost for CSKA coach Leonid Slutsky as his side claimed the first of their Group B campaign. Despite the scoreline, Turkey's Trabzonspor posed a constant threat from set-pieces and enjoyed a great deal of possession, but CSKA were able to neutralise all their attacks.
"It was much tougher to win today than it may appear looking at the scoreline," CSKA manager Leonid Slutsky said. "But we played confidently keeping everything under control and didn't allow Trabzonspor to create serious threats except one occasion at the start.
"Taking into consideration our personnel problems we played very well. And I'm very glad that we managed to keep a clean sheet."
Trabzonspor almost scored the opener when Adrian Mierzejewski flicked the ball on to Alanzinho, but the midfielder failed to get the touch to send it past CSKA goalkeeper Vladimir Gabulov. The loose ball fell to Halil Altintop, but he could not get enough power on his shot.
CSKA went close from Alan Dzagoev's free-kick after Arkadiusz Glowacki was carded for a challenge on Doumbia just outside the area, but the ball went wide of the left post.
Glowacki thought he had broken the deadlock just before the half-hour when he lunged onto the end of Mierzejewski's free-kick and found the back of his net, only to see the offside flag raised.
But it was Doumbia who opened the scoring a minute later after a great counter-attacking move which saw him put through on goal by a back-heel from Love which split the defence and allowed the Ivorian to shoot home powerfully from close range.
After the break, Aldonin missed the chance to double CSKA's lead when Gustavo Colman lost his footing, the midfielder shooting wide from 20 yards. Mierzejewski then missed a good chance to equalise for Trabzonspor from point-blank range in the 58th minute.
Love turned provider again when he surged down the right and lofted an inch-perfect cross to substitute Cauna who beat Zengin with a left-footed volley from just inside the area in the 76th minute.
The goal, Cauna's first of the season, came as Trabzonspor were starting to dominate possession, and the 23-year-old Latvian almost scored his second when his volleyed strike hit the post six minutes from time.
It was the excellent Doumbia who had the final word, neatly beating two defenders and wrong-footing Zengin to allow him fire home with four minutes left.