As the division resumed after a mid-season break of three months, Lokomotiv moved to the summit with a 2-1 home win over Krylya Sovetov on Monday.
Senegal striker Dame N'Doye scored his 11th league goal of the season to give Lokomotiv the lead in the 18th minute.
And substitute Roman Pavlyuchenko came off the bench to set up Magomed Ozdoev for Lokomotiv's second with just 13 minutes remaining, before Stanislav Dragun pulled back a late consolation for Krylya in the 87th minute.
Anzhi, who have had to deal with a mass exodus of players sparked by owner Suleyman Kerimov's decision to withdraw the majority of his funding, have surprisingly reached the last 16 of the UEFA Europa League.
But their league form had been miserable up until this point, with Alexander Bukharov's 84th-minute goal giving his side a rare win.
Ural triumphed 1-0 at Krasnodar on Saturday thanks to Gerson Acevedo's first-half strike while on the same day, Spartak Moscow were shocked at Terek Grozny, losing by the same scoreline.
CSKA led 2-0 at the break thanks to a double from Seydou Doumbia, but Kevin Kuranyi's goal four minutes into the second half changed the course of the match.
Christopher Samba levelled just before the hour-mark and two late Yuri Zhirkov goals sealed Dinamo's victory.
Other results saw Fegor Ogude strike twice in Amkar Perm's 5-1 thrashing of Volga and also on Monday, Rostov played out a goalless draw with Kuban Krasnodar.
