The meeting, which took place at the Akhmat Arena stadium in Grozny, ended 3-1 in favor of Spartak.
The winners included a double on the account of Zelimkhan Bakaev, another goal on the account of Andre Schurrle, who scored his first goal in the RPL.
Ablai Mbengue was the only accurate hit by Akhmat.
Spartak won a second victory in the championship of Russia - 2018/19, Akhmat suffered a third defeat at the start of the season.
Earlier it was reported that Spartak offered € 9 million for a Nice player.