Spartak emerged victorious from a fiery derby in the capital, Dmitri Kombarov's penalty in the 61st minute settling the game in the visitors' favour, before CSKA's Kirill Nababkin and Spartak's Sergei Parshivlyuk each saw red in the third minute of injury time.
CSKA's defeat means Zenit are the only team in the league with a 100 per cent record, although Andre Villas-Boas' men needed a 31st-minute penalty from Hulk to seal a 1-0 win over newly promoted Ufa, as they attempt to regain the title they last won in 2011-12.
Dinamo Moscow leapfrogged CSKA into second with a 2-1 victory at Arsenal Tula, Douglas and Kevin Kuranyi on target in the first half before Ivan Ershov gave Arsenal false hope with a 47th-minute strike.
Rubin Kazan are still without a win after they played out a 1-1 home draw with Lokomotiv Moscow, Gokdeniz Karadeniz's 31st-minute penalty earning the hosts a share of the spoils after Aleksey Miranchuk had put Lokomotiv ahead five minutes earlier.
Torpedo Moscow claimed their first win of the campaign with a 2-0 success at Ural, while Krasnodar came away from their trip to Rostov with a victory by the same scoreline.
Elsewhere, Romanian attacker Gheorghe Bucur scored in the second minute of injury time to give Kuban Krasnodar a 1-0 triumph over 10-man Amkar Perm, who saw Fegor Ogude sent off, and Terek Grozny beat Mordovia Saransk 1-0.