City threw away a two goal lead in Moscow as their atrocious run of form in the Champions League continued, to leave them staring down the barrel of a group-stage exit for the third time in four years.
Aguero, who scored four times against Spurs in the Premier League on Saturday, continued his goalscoring form when he found the net on 29 minutes.
The magician, Silva managed to beat the offside trap and slipped the ball through to Dzeko. The Bosnian unselfishly squared to Aguero, who slotted the ball into the empty net.
City made it 2-0 on 38 minutes. Yaya Toure, who was racially abused in the corresponding fixture between the two teams a year ago, played a floated pass to Zabaleta.
The Argentine knocked the ball down to Aguero, who mis-kicked his shot, but Milner followed up to tap into an empty net.
Milner could have extended his side's lead six minutes before halftime, but the midfielder's shot hit the post.
In to the second half and CSKA went close to reducing the deficit when Roman Eremenko's 25-yard effort got the better of Hart but landed on the roof of the net.
In the 65th minute a finely-worked move did put them firmly back in the match, Musa drove the ball across Hart's goal for Doumbia to pounce.
Pellegrini replaced Dzeko with Jesus Navas with 20 minutes remaining, but in a hugely disappointing finish for City, the Russians levelled from the spot after Kolarov brought down Doumbia, with Natcho converting the penalty. Hart expressed his frustration at the penalty decision;"I don't think it was a foul but Aleks gave the referee a decision to make. We thought it was the wrong one, but a lot more could have been done before that to get the result."