City picked up where they had left off in their 7-0 demolition of Norwich City at the weekend, with Aguero scoring twice and Negredo adding another to put the home side 3-0 up inside 30 minutes at the Etihad Stadium.
Defensive inattention allowed Seydou Doumbia to twice reduce the arrears, but Negredo completed his treble in the second half to send City into the last 16 for the first time in the Champions League era.
Victory left Manuel Pellegrini's side six points clear of CSKA with two games to play in Group D, but they cannot be overtaken by the Russian champions due to a superior head-to-head record.
"It is the first step, but it's an important one as the team has not qualified before. We have done that now," said City manager Pellegrini.
"The most important thing was that we can play the last two games of the group and try to come top. Then we can see in February who we get and anything can happen in the knockout stage."
CSKA, who were hit with a partial stadium ban by UEFA for racist chanting aimed at City midfielder Yaya Toure in the reverse fixture, are left to scrap over a Europa League place with Czech side Viktoria Pilsen.
"It's obvious we made a lot of mistakes," said CSKA coach Leonid Slutsky. "With a team as tough as Manchester City, you have to be alert because they can be fatal in a split-second."
Pellegrini kept faith with the team that had annihilated Norwich on Saturday, which meant that Joe Hart was once again on the bench with second-choice goalkeeper Costel Pantilimon in goal.
CSKA were missing a number of first-team players due to injury, including Alan Dzagoev, Vasili Berezutsky and Mario Fernandes, and there were less than three minutes on the clock when they fell behind.
Former Manchester United player Zoran Tosic was in the visitors' XI and will not have endeared himself to fans of his old club by sliding in on David Silva and conceding a penalty from which Aguero put City ahead.
With Silva and Samir Nasri pulling the strings, some of City's approach play was delightful, and their second goal, in the 20th minute, was a fine effort.
Nasri clipped a penetrative pass down the inside-left channel and Aguero left Aleksei Berezutsky for dead with a superb, sharp turn before steering home his eighth goal in five games.
Pantilimon had an anxious moment when he flapped at a deflected free-kick, but after Toure had curled narrowly wide, Negredo touched in Aguero's low cross to make it 3-0.
There was further bad news for CSKA when Ahmed Musa had to go off with an injury, but Doumbia gave the visitors a glimmer of hope when he rounded Pantilimon to pull a goal back in first-half stoppage time.
City were quick to restore their three-goal advantage in the second half, however. In the 51st minute Toure floated a delicate pass over the top of the CSKA defence and Nasri knocked a volleyed pass into the path of Negredo for the Spaniard to walk in his second goal.
Silva departed to a standing ovation with 25 minutes remaining, but once again City were guilty of presenting their opponents with a foothold in the game.
Gael Clichy was at fault on this occasion, hauling Doumbia down after being nutmegged on the left-hand edge of the City area, and the Ivorian converted the resulting penalty to reduce the arrears.
Visiting goalkeeper Igor Akinfeev saved from Negredo, Aleksandar Kolarov and Aguero, before Negredo completed his first City hat-trick in injury time with a back-post header from a James Milner cross.