The meeting, which took place at the Akhmat-Arena, ended with a 2: 0 victory for the guests.
Remi Cabella and Vladimir Ilyin scored goals.
From the 65th minute of the meeting, the hosts played in the minority due to the removal of Zoran Nizic.
Krasnodar scored 13 points and moved up to sixth place in the RPL standings.
Akhmat remained on the 11th line.
The club from Grozny has nine points to its credit.
Earlier, Krylya Sovetov defeated Rostov in the RPL match with six goals.