The meeting, held in Khimki, ended with a score of 1: 1.
Kamil Mullin scored for Rotor in the 32nd minute, assisted by Danil Stepanov.
Khimki responded with a goal by Alexander Lomovitsky, who scored in the 56th minute with Arshak Koryan's pass.
Both teams extended their unbeaten streak at the start of the season.
In the seventh round, Khimki will play away from Ural Yekaterinburg, and Rotor will take over Krasnodar in their field.
Earlier it was reported that Spartak beat Arsenal and rose to first place in the RPL table.