Aras Ozbiliz opened the scoring for the hosts in the 40th minute, and two further goals in seven second-half minutes sealed the win for Valeri Karpin's team.
Dmitri Kombarov struck first before Sergei Parshivlyuk sealed the win just before the hour mark, sending CSKA to their first defeat of the season.
After their UEFA Champions League defeat to Atletico Madrid on Wednesday Zenit bounced back with a league win as they cruised to a 4-0 win away at Rostov.
Luciano Spalletti's side struggled to break the deadlock in the opening half but were ruthless after the break.
Danny opened the scoring six minutes after the break before Andrei Arshavin, Hulk and Viktor Faizulin all scored to seal the win.
Each of Spartak, Zenit and CSKA are on 20 points through nine games.
Locomotive Moscow kept themselves within touching distance of the top three with a 3-1 over Dinamo Moscow.
Dame Ndoye opened the scoring for Locomotiv early in the second half, but their lead lasted eight minutes as Christian Noboa levelled for Dinamo on the hour mark.
The visitors to Dinamo's Arena Khimki were handed a boost in the 73rd minute when Douglas conceded a penalty, earning a red card in the process.
Alexander Samedov converted the spot kick, and Sergey Tkachev scored a third to secure the win in injury time.
Tom Tomsk got their first win of the season as they came from behind to beat Rubin Kazan 2-1 away from home.
Salomon Rondon had opened the scoring for Rubin but Alexander Ryazantsev's red card in the 33rd minute changed the game.
His dismissal led to Kirill Panchenko converting a penalty, but the relegation-placed club had to wait until the closing minutes for Maksim Bordachev to find the back of the net to give them a valuable three points.
That result dropped Terek Grozny to the foot of the table as they lost 1-0 to Krasnodar, with Pavel Mamaev's 14th minute strike enough to take all three points and leave Grozny chasing their first win of the season.
Anzhi are also searching for their first win after they fell to their fifth defeat of the season against Volga in a 2-1 away defeat.
The hosts raced into a two-goal lead inside the opening 21 minutes, and although Anzhi pulled a goal back, they were unable to find another to take something from the game.
Elsewhere Kuban Krasnodar fell to a 3-0 defeat at home to Amkar Perm, and Krylya Sovetov drew 1-1 with Ural.
