Nick Calathes top scored with 15 points and the Greek side never looked back after a strong second quarter helped them go in at the break 41-36 in front.
Kostas Kaimakoglou was a menace in the paint as he scored 12 points and had seven rebounds while Dimitris Diamantidis and Sarunas Jasikevicius also scored double figures.
Devin Smith and Keith Langford top scored for Maccabi with 14 but disappointed from three-point range shooting a combined 1-9. In total the hosts were just 4-23 from beyond the arc.
Game five will be played next week in Athens.
On Friday, Olympiacos and CSKA Moscow will have a chance of reaching the Final Four as they play game fours.
Olympiacos just need to win at home against Montepaschi Siena to punch their ticket while CSKA travel to the Basque Country to face Bilbao.
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