German Wings fly from both Berlin-Schonefield and Cologne Bonn to Moscow-Vnukovo. I've just tried putting some sample (mid-February) dates into their booking system. All of the flights I found were between US$80 and US$110 + taxes and charges (which are US$36.87 outward and US$23.36 return). That seems fairly reasonable to me (and, of course, it might be possible to find even cheaper flights with a bit more hunting on the website):
http://www24.germanwings.com
DBA fly from Berlin-Tegel to Moscow-Domodedovo. I've just found some flights, for �77in each direction. (Taxes & charges �45.38 out, �29.81 return):
https://www.flydba.com/app/fb.fly?l=en
(I've just noticed that the actual flight operator is Germania Express but you can still book through the DBA website).
DBA (or their partners) also fly direct to Moscow-Domodedovo from Cologne-Bonn, Dusseldorf (Nordrhein-Westfalen), Frankfurt Main International, Hamburg, Munich (Franz Josef Strauss), Nuremberg and Stuttgart-Echterdingen so you'll have plenty of options open to you.
Hoping something here is useful to you,
Chris