Zenit St Petersburg began the defence of their Premier League title with a routine 2-0 victory over Amkar Perm.
Aleksandr Kerzhakov put his Euro 2012 struggles behind him to get both goals in the win, curling in the first eight minutes before the break and then lashing in a penalty just after the hour mark.
Big-spending Anzhi Makhachkala got what they hope will be a sustained challenge at the top underway with a 2-1 win over Kuban Krasnodar, but it did not come without a stutter.
With their season just four minutes old they trailed as Carlos Pinto put through his own net, but Samuel Eto'o bagged the equaliser in the 31st minute before Lacina Traore scored the winner just before half-time.
Luis Caballero scored an 82nd minute penalty to give Krylya Sovetov a 1-1 draw at home with Terek Grozny.
Caballero scored after Dmitry Yatchenko handled inside the area. The visitors had led through Oleg Ivanov's long-range effort in the 56th minute.