The Argentinian continued his rich vein of form with a quickfire double to settle a tricky Group D encounter after former Manchester United player Zoran Tosic opened the scoring.
Despite coping well with the much-criticised Khimki Arena pitch, City squandered a number of chances to make the game safe and were left hanging on, with Joe Hart saving saving from Keisuke Honda at the death.
But they survived CSKA's late rally and exerted enough control overall to suggest they could all but secure a last-16 spot with a repeat win at the Etihad Stadium in a fortnight.
On a sour note, however, it did sound as if some monkey-chanting was directed at Yaya Toure from a section of the home support.
The patched-up surface, described as "unbelievable" by City boss Manuel Pellegrini was sandy, bobbly and bare in patches.
City although it slowed City's style, they soon asserted themselves against the out-of-form Russian champions, who had lost five of their previous seven games.
The hosts were also forced into an early change as defender Vasili Berezutski left the field and was replaced by his brother Aleksei Berezutski.
City's first chance came as a corner by David Silva was flicked on by Aguero just beyond Toure.
Aguero then failed to connect with a volley from a Pablo Zabaleta cross after a good move involving Jesus Navas and Toure.
CSKA showed some attacking intent as the highly rated Keisuke Honda was picked out by a long ball.
The Japan international's control initially let him down but he got a second chance and had a shot blocked by Aleksandar Kolarov.
City began to threaten again as Silva weaved his way into the area and Aleksandar Kolarov whipped in a cross which was diverted straight at Igor Akinfeev by Alvaro Negredo.
It came as a surprise when CSKA grabbed the lead, against the run of play, after 32 minutes.
Akinfeev's long ball was headed on by Honda and Tosic raced through, displaying skill he did not show in his spell at Old Trafford, which amounted to five substitute appearances, to lob Hart.
The goal again highlighted City's defensive vulnerabilities in the absence of captain Vincent Kompany, with midfielder Javi Garcia in the back line, but it jolted them into action.
Their response was immediate as they attacked down the left and Silva delivered a fine ball into the area.
Aguero edged ahead of his marker to claim and, although the ball got trapped slightly under his foot, he took a touch to dig it out and then slid it home.
It was not long before City had a second, Aguero on target again to head a Negredo cross past Akinfeev from close range after confusion in the home defence from a throw-in.
It was the Argentinian's eighth goal in his last six games.
City could have had a third before the interval as Navas had a dangerous cross claimed by Akinfeev and the goalkeeper produced a fine one-handed save to keep out a Silva free-kick.
City thought they did have a goal number three in the early moments of the second half but Negredo's close-range effort was ruled out for handball.
Moments later Toure headed powerfully at goal but Akinfeev saved low to his right and Kolarov curled a free-kick just wide.
Silva had a good chance just after the hour when Aguero allowed Kolarov's cross to run past him but the inrushing Spaniard lost his balance attempting a first-time shot. Toure also tried his luck from a free-kick wide on the right but Akinfeev parried over the bar.
CSKA tried to produce a rousing finish and City survived a scare when a superb strike from 18 yards, into the top corner, by Ahmed Musa was disallowed for a foul.
Musa troubled City again with a weaving run but Hart was equal to his shot.
Honda had a golden chance to equalise in stoppage time after chesting down a cross but Hart got in the way to block his volley at point-blank range.
Source: Manchester City MAD