After cruising to an 88-73 home win in Greece, Georgios Dikaioulakos and Co travelled to Ramla and prevailed 91-72.
Kathryn Ann Gearlds poured in a game-high 23 points for Athinaikos, who trailed 15-10 early in the contest but then stamped their authority on proceedings.
Gearlds had 11 points by the time the visitors had gone into a 21-15 lead.
At the end of the first quarter, Athinaikos were on top 30-20 and for all intents and purposes, they had sealed their progression with a 25-point lead on aggregate.
Greece international center Polymnia Sarekgou, who played for her country at the 2004 Olympics, had eight points by the end of the opening frame for Athinaikos.
Athinaikos then blew the game wide open and claimed an easy win on the night.
Katia Levitsky led Ramla with 18 points and 10 rebounds.