Aguero struck twice late in the first half after Zoran Tosic had put CSKA ahead in the 32nd minute. The Argentine quickly levelled with a low strike from David Silva's cross and then headed Alvaro Negredo's clever delivery past Igor Akinfeev.
City wasted several chances to add to their lead after the break and almost paid the price in stoppage time when only a brilliant save from Joe Hart denied Keisuke Honda an equaliser.
The English side's victory, however, was marred by racist abuse from the stands aimed at City's Ivorian midfielder Yaya Toure.
"I told the ref. I think it was unbelievable and very sad," Toure told Sky Sports. "I think UEFA have to do a lot to try to stop it."
City moved on to six points from three games in Group D, level with Bayern Munich who host winless Viktoria Plzen in a later kickoff. CSKA are third on three points.
Poor away form, with five defeats out of six, was a feature of City's group stage exits in their last two Champions League campaigns but they have now won twice on the road following a victory in Plzen last month.
DIFFICULT PITCH
Manager Manuel Pellegrini said City were well placed to progress.
"I'm very happy; it was a very difficult game for us," he said.
"This pitch made it very difficult to play football - to have three points from this match is very important for our future in this group.
"It's important, it's not the last game, it's very important that we have the next two games at home - we go into them knowing that if we win, we qualify."
CSKA, in poor domestic form having lost three successive Russian Premier league games without scoring, broke the deadlock
with a route one goal at the Khimki Arena.
Akinfeev pumped the ball forward, Honda outjumped Javi Garcia to flick the ball on and Serbian international Tosic, once of Manchester United, nipped in to lift the ball over Hart.
Their lead lasted all of 90 seconds, Aguero pouncing to fire home after Sergei Ignashevic had failed to deal with Silva's cross from the left under pressure from the Argentine.
City struck again three minutes before the break, Silva linking up with Negredo who deftly flicked a cross into the danger area which Aguero stooped to head home.
CSKA thought they had levelled 10 minutes from time when Ahmed Musa beat Hart with a fierce shot from the edge of the area but the whistle had already been blown for a foul on Toure.
The Khimki Arena pitch, CSKA's temporary home with the Luzhniki stadium being redeveloped for the 2018 World Cup, was passed fit to play, despite heavy rain this month which left large threadbare areas.
CSKA were ordered by UEFA to stage their home game against Plzen on October 2 in St Petersburg due to the condition of the playing surface.
(Writing by Justin Palmer, editing by Alison Wildey)
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