Hugo Almeida put Bremen ahead after 32 minutes, but second-half goals from Ieroklis Stoltidis, Christos Patsatzoglou and Darko Kovacevic secured the Greek team's victory.
Bremen fell to 0-2 while Olympiakos now has one win and one draw.
Turkey has found itself in a circle of countries subject to US and European sanctions. Are they dangerous for Ankara? What is Turkey going to do in response?