Krunoslav Simon led all scorers with 24 points at Moscow's Mytishchi Arena.
Shane Larkin had 20, Tibor Pleiss produced 18 and Adrien Moerman added 14 points and 7 rebounds.
Jordan Mickey and Janis Timma each scored 13 points for Khimki Moscow Region.
Thursday results in EuroLeague:
Khimki Moscow Region - Anadolu Efes: 105-77
Bayern Munich - CSKA Moscow: 81-89
TS Systems Baskonia Vitoria-Gasteiz - Panathinaikos OPAP: 93-72