With second-placed Anzhi Makhachkala held at home by Krylya Sovetov, CSKA enhanced its title prospects thanks to a 17th-minute goal from attacking midfielder Alan Dzagoev.
It was a bad day for Anzhi Makhachkala but it might have been worse.
It had a one-man advantage from the 37th minute of its match after Krylya Sovetov had Alexander Amisulashvili sent off, but the visitor which stands third bottom in the table then took a 64th-minute lead through Sergey Kornilenko.
Anzhi had a long trip to
However it at least salvaged some reward, with
Third-placed Zenit St Petersburg also went out of the Europa League in midweek as Swiss side Basel took its scalp, but Zenit returned to winning ways, edging a home tussle with Mordovia Saransk by a 1-0 margin.
Striker Hulk put Zenit ahead after 55 minutes, and Mordovia was reduced to 10 men six minutes later as