The loss leaves the Moscow club in bottom place in the four-team group with a single point from six games.
CSKA, playing without either of their two Brazilian stars - Daniel Carvalho and Vagner Love - took the lead in the 30th minute when Edu put through his own goal.
However, Fenerbahce, needing a victory to ensure progress to the competition's play-off stage, quickly drew level with a well-struck goal from their own Brazilian star, Alex De Souza, in the 32nd minute.
That goal saw the Turks lift their game, and Ugur Boral put the side into the lead just before the break, much to the delight of the home fans.
CSKA's goal led a charmed life in the second-half, but it was Boral who made sure that Fenerbahce made it through to the play-off stages for the first time in their history, a looping header beating the Russian side's keeper, Akinfeyev, in the last minute of play.
The game rounded off a disappointing 2007 for CSKA, a season in which the 2003, 2005 and 2006 Russian Premier League champions only managed third place in the league, losing their domestic title to Zenit St. Petersburg.
