The meeting, which took place in Moscow, ended with a score of 2: 0 in favor of the home team.
Dynamo's victory was brought by goals from Maximilian Philip, who converted a penalty in the 42nd minute, and Nikolay Komlichenko, who scored from Sebastian Szymanski's pass in the 45th minute.
In the fourth round, Dynamo will play on the road with Arsenal Tula, and Rostov will play Ufa on a visit.
Earlier it was reported that the double of Odis Roshi helped Akhmat to defeat Rotor in the third round of the RPL.