The meeting, held in Moscow at the VEB Arena, ended 3-0.
The victory came to the army team goals Mario Fernandez, Fedor Chalov and Nikola Vlasic.
In the next round, CSKA will play with Tula Arsenal away, while Akhmat will host Tambov on its field.
Earlier it was reported that the Akhmat coach Rashid Rakhimov spoke about the injury of Denis Glushakov.