The away side made most of the early running, however, with Aleksandar Kolarov firing high and wide of the crossbar from outside the box, although Zoran Tosic did hit the side-netting for CSKA with 12 minutes on the clock.
Sergio Aguero might have tested the home side's goalkeeper with a strike moments later, but his volley moved harmlessly wide of the post. Doumbia threatened with his pace down the other end in the next attack, but his final touch allowed City defender Matija Nastasic to clear the danger.
Aguero had another opportunity from a header after 22 minutes, but the Argentine could only loop his effort high and wide of the crossbar, before Alvaro Negredo missed the target with a long-range strike.
CSKA were ahead after 32 minutes when Tosic lifted his effort over Hart from inside the box, but City were level two minutes later when Aguero turned a David Silva cross into the back of the net.
Aguero was on target once more in the latter stages of the half, as he headed a Negredo cross into the back of the net to leave City ahead at the interval.