The Premier League side had exited the competition at the group phase for the past two seasons, but back-to-back wins over CSKA in Group D sent City into the last 16 with two games to spare.
Aguero was in scintillating form at the Etihad Stadium as he opened the scoring from the penalty spot after just three minutes before a sharp turn and shot on 20 minutes doubled the lead.
The Argentina striker then turned provider by rolling the ball across goal for Negredo to score on the half-hour mark as City threatened to repeat the seven goals thumped past Norwich City at the weekend.
CSKA pulled one back just before half-time when Seydou Doumbia rounded goalkeeper Costel Pantilimon, who again got the nod ahead of Joe Hart, before Negredo added his second of the game early in the second half.
Doumbia scored again from the penalty spot on 71 minutes after he had been pulled back by Gael Clichy before Negredo headed home in the final seconds to cap a historic evening for Manuel Pellegrini’s men.
After the meeting between the two clubs in the Russian capital a fortnight ago was soured by racist chanting aimed at Yaya Toure, there was also focus on the crowd.
City fans were quick to burst into a chant of support for Toure and followed that up by informing their CSKA counterparts, in crude terms, that they regarded them as racists.
On the field City were quickly into their stride as the same side that started Saturday’s 7-0 win over Norwich picked up where they left off, which meant Hart was on the bench again.
Less than two minutes had gone when David Silva tricked his way into the CSKA box and was brought down by former Manchester United winger Zoran Tosic.
Aguero clinically dispatched the penalty to move clear of Francis Lee as City’s record goalscorer in Europe.
CSKA capitalised on the vulnerability that remains in the City defence in the continued absence of Vincent Kompany to carve out a chance for Doumbia but he blazed over.
City began to assert themselves more as Toure shot over from a free-kick and Silva combined with Samir Nasri before lashing into the side-netting.
Aguero’s second came as he took a Nasri pass and brilliantly turned Aleksei Berezutski with a deft touch before guiding a shot past Igor Akinfeev.
Negredo claimed the third on the half-hour as he found Aguero wide and then received a perfect return pass into his path from the Argentinian to tap in from six yards.
An Aguero overhead kick was blocked and Negredo narrowly failed to turn in another good cross from his strike partner.
CSKA broke the procession on the stroke of half-time as Pontus Wernbloom split the City defence with a superb through-ball and Doumbia glided around Pantilimon to pull one back.
It may have raised more questions over the defence but they could wait for another day as City resumed normal service in the second half.
Nasri met a Toure pass with a superb first-time flick that gifted Negredo another tap-in.
As Bayern Munich took the lead against Viktoria Plzen in the other game in the group, City were cruising to the next stage but they had a jolt as Clichy tripped Doumbia.
Toure’s Ivory Coast team-mate got up to send Pantilimon the wrong way from the spot and reduce the arrears.
It was almost immediately cancelled out as Negredo narrowly failed to claim his hat-trick with a shot that flew inches over the bar.
The Spaniard went close again after substitute Jesus Navas caused more defensive uncertainty but his close-range effort was deflected wide.
City grabbed the fifth goal their superiority deserved as Negredo wrapped up the scoring in injury-time by heading home a cross from James Milner to complete his hat-trick.