The Superleague Greece title-holders stunned Juventus 1-0 in the UEFA Champions League thanks to Pajtim Kasami's first-half strike with goalkeeper Roberto Jimenez producing a number of fine saves after the break to deny the Italian visitors in Piraeus.
The victory was Olympiacos' second in Group A, taking them level with Atletico Madrid at the top of the standings, although the Greeks trail the La Liga champions on goal difference.
Olympiacos started their Champions League campaign with a 3-2 triumph over Atleti and Marinakis argued their wins against two of the finest clubs in Europe was a big statement of their own quality.
"It makes history and see how the players reproduce. They believe in themselves and give the answers on the pitch," Marinakis told Olympiacos' website.
"What we want and why we work every day is to be able in such games that [the players] give their best. That was staggering today...it was flawless."
Olympiacos' technical director Christian Karembeu added it was important for the club to respond after suffering a 2-0 loss away to Malmo on the last matchday.
"We must respect the opponent, Juventus. That is why it is important and this is a great victory," the former France international and Olympiacos midfielder said.
"Coming after the defeat by Malmo, so I wanted to do something good in today's match and we are very happy that we did."
Next up for Olympiacos is the 'Derby of the Eternal Enemies' versus Panathinaikos in the league on Sunday.
Olympiacos sit third in the Superleague standings on 13 points, three ahead of their arch-rivals.
"It's a different atmosphere. Another league than the UEFA Champions League but this win definitely gives us the confidence to achieve something good against Panathinaikos," Karembeu said.
Olympiakos have not won in front of their home fan against Panathinaikos since 2011.
