The Greek side entered the final period tied with their Turkish opponents but a blistering 24-5 scoring run effectively settled the outcome.
The result sees Olympiacos draw level with Andalou with a 2-1 record in Group E.
Henry Domercant led the Russian side with 16 points while a sterling defensive performance from the hosts limited Milan to their lowest total in the EuroLeague.
And in an all-Spanish affair in Group F,
Sergio Rodriguez was the star for Madrid with 20 points and seven assists as his side opened up an early double figure lead and never looked like giving it up.