Ivory Coast striker Lacina Traore headed Guus Hiddink's men ahead in the 57th minute and Morocco international Mbark Boussoufa added a second 20 minutes later after great work by Cameroon striker Eto'o.
CSKA, who beat Anzhi 1-0 in their first meeting this season in August, had midfielder Alexander Cauna sent off after a second booking late in the first half and rarely troubled the home side.
"It was a high tactical game with both teams trying to play to their strength," Hiddink told Russian television NTV.
"But we had an extra man in the second half and we tried to force the game to them. We scored two goals and in the end could have had another one."
After the second goal, an emotional Eto'o ran to the stands to celebrate with the home fans.
"The fact that we beat the league leaders makes all of us very happy," said the four-times African Footballer of the Year, who joined Anzhi last year on a three-year deal which pays him a reported annual salary of 20 million euros.
"After that second goal I was overcome with emotions and wanted to share my joy with our fans. If [security] didn't stop me I would have just kept on running and running."
The win extended Anzhi's unbeaten run to five games and moved the big-spending club from the volatile North Caucasus region level on 40 points with CSKA, though the Muscovites remained in first place because they have won more matches.
Spartak, who have now lost three in a row, sacked coach Unai Emery last Sunday following a 5-1 home thrashing by their bitter city rivals Dynamo, replacing the Spaniard with the club's general director Valery Karpin.
Luciano Spalletti's team, who were held to a 1-1 home draw by CSKA behind closed doors last Monday, now face Anzhi at an empty Petrovsky arena in St Petersburg next weekend before the Russian league takes a three-month winter break.
"It's a bit unfortunate for us to take a long break now because we have been playing very well recently," said Hiddink, whose team have also reached the Europa League knockout stage.
"But there's nothing we can do about it. We just have to accept it and come back even stronger after the break."
