Manuel Pellegrini guided his team to the knockout stages for the first time with two games to space thanks to Bayern Munich beating Viktoria Plzen in the group's other game
Argentina striker Sergio Aguero scored twice in the first half to become City’s all-time leading scorer in European football and put the club on course to qualify from Group D.
Aguero took his tally to nine goals in his last six games in the process and he then set up Negredo for a third goal before Seydou Doumbia pulled one back just before the break.
Spain striker Negredo added a fourth goal early in the second half before Doumbia added his second of the night from the penalty spot.
Negredo then completed his hat trick in stoppage time as City qualified for the knockout stages, courtesy of their head-to-head record against the Russians.
City thrashed Norwich 7-0 in the Premier League on Saturday, so it was no surprise that Manuel Pellegrini named an unchanged side – the first time he has done so as City boss - with Costel Pantilimon again preferred to under-fire England goalkeeper Joe Hart.
CSKA headed into the match having won its last three domestic games following its defeat to City last month and it was also unchanged.
The pre-match talk was dominated by the alleged racial abuse suffered by City midfielder Yaya Toure in the first meeting between the sides last month that resulted in UEFA deciding to close part of CSKA's Arena Khimki for their clash with Bayern Munich.
But City was focused on the task of qualifying and it was in front after just three minutes, when Zoran Tosic upended David Silva and Aguero's spot kick evaded the outstretched arm of goalkeeper Igor Akinfeev diving to his left.
Aguero then doubled City's lead when he sublimely turned his marker inside the area before dispatching a measured right-foot strike into the bottom-left corner of Akinfeev's goal after just 21 minutes.
The lively Argentinian then turned provider on the half-hour mark when he took a pass from Negredo in his stride and then picked out the Spain striker at the back post for a simple tap-in.
But it was CSKA that had the final say in the first half when Pontus Wernbloom slipped the ball through for Doumbia and the striker rounded Pantilimon before pulling a goal back in stoppage time.
Any hopes of a CSKA comeback were dashed six minutes into the second half, though, when Toure picked out Samir Nasri with an incisive pass and the midfielder set up Negredo for another simple finish.
Doumba was a real handful and he scored his second of the night from the spot after Gael Clichy was adjudged to have fouled him to make it eight goals in his last 10 games.
But Negredo had the final say as he headed home at the back post to cap a memorable night for City.