Brown Ideye netted in the 79 minutes to ensure victory for his team.
Ideye Brown scored from an almost impossible angle as the Greek champions built on their Arsenal win with another away victory.
Olympiacos took the points at Dinamo Zagreb that many predicted following their triumph at Arsenal, but victory was hard-fought in Croatia.
The home side were twice denied by the frame of the goal and ultimately Ideye Brown was the difference between the Group F rivals. With 11 minutes remaining he cut in from the left and somehow squeezed the ball between Eduardo and the post from a seemingly impossible angle.
Yet it had been Dinamo that had made the early running, with their supporters’ chant “we want another win” as uplifting as it was unsubtle. El Arbi Hilal Soudani came close to going some way to meet their demands but could not quite connect with a cross and slowly the visitors came into it.
The Greek champions, ever watchful, began to commit men forward but were almost stung at the other end early in the second half as Domagoj Antolić punched a hole in their defence and rattled the upright. Olympiacos hit right back on the break with Ideye, sliding in at the far post, not able to turn the ball in.
It was a similar story later in the half as, moments after a golden chance for Marko Rog that came back off the woodwork, Ideye found the net.
Olympiacos moved alongside Bayern on six points, three ahead of Dinamo and Arsenal, courtesy of Ideye Brown’s goal with 11 minutes to go – giving the Greek champions, who had lost all three road trips last term, a second straight away win in the group.