Maroussi used a scoring spurt at the end of the first half to take control against Serbians Vojvodina propel themselves to an 80-64 triumph.
Vojvodina gave as good as they got early on, and the game was tied at 19-19 at the end of the first quarter.
But Maroussi got their noses in front in the second and when Renaldas Seibutis, who shone at Olympiacos last season under coach and fellow Lithuanian Jonas Kazlauskas, scored to complete a 9-0 run at the end of the first half, Maroussi led 45-31.
Christopher Thomas' three-ball at the start of the third quarter continued the run and extended the advantage to 48-31.
Instead of caving in, though, Vojvodina dug in their heels and battled back.
Cedomir Vitkovac split two from the line and on the next trip down the floor made a jump shot.
That started an 11-0 surge that was capped by Vitkovac with two more free throws.
When Vitkovac made one of two from the charity stripe with 3:23 to go in the third quarter, the hosts trailed 50-45 but they would get no closer.
Maroussi reeled off the next 12 points to lead 62-45 with 9:36 to go in the final quarter and they stayed in control the rest of the way.
Seibutis had 18 points and five rebounds for Maroussi, who shot the ball well all over the court.
They finished 30 of 44 (68.1%) inside the arc, four of seven (57.1%) beyond it while also nailing eight of nine (88.8%).
Vojvodina were 13 of 22 (59%) from the line, and they were outrebounded 31-19.