Rasmus Elm's penalty midway through the first half put CSKA ahead against 11th-spotted Amkar, and
Ahmed Musa doubled the advantage before Aleksandrs Cauna added further gloss to the scoreline on the stroke of full-time.
Big-spending Anzhi Makhachkala, meanwhile, lost ground in the race for top spot as it failed to break down 12th-placed Rostov.
In the day's other game, Kuban Krasnodar was a comfortable 3-0 winner at bottom-of-the-table Mordovia Saransk and climbed to sixth position as a result.
Pavel Stepanets' own goal in the 18th minute set the visitor on its way, with
Balde Ibra and Aras Ozbiliz on target either side of the interval to seal the rout.