Manuel Jimenez's Greek Cup winners claimed all three points thanks to Leonardo's 38th-minute penalty at the Olympic stadium.
AEK, who started the mini-league tournament involving the teams who finished the season placed second to fifth with one point, now have four points.
Panathinaikos, who started with three points, dropped down to second after Jesualdo Ferreira's team were beaten 2-1 by PAOK Salonika.
Goals from Stefanos Athanasiadis and Nabil El Zhar gave PAOK a two-goal lead against a lacklustre Panathinaikos side for whom Djibril Cisse pulled a goal back with 11 minutes remaining.
The next round of matches are scheduled for Thursday with Olympiakos Volos hosting PAOK and AEK facing Panathinaikos in an Athens derby.
Olympiakos Piraeus sealed their 38th Greek title in March.
