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.
Anadolu Efes gained their fifth win in the EuroLeague while Khimki Moscow Region continued to struggle, losing seven times in nine games.
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
