Having won the first leg 64-58 in Russia, the Athens outfit returned home and rode a strong start to a 60-55 triumph.
George Dikeoulakos' team will now take on another Russian side, Nadezhda, for the EuroCup women crown.
There has been a buzz about the women's game in Greece since the national team clinched a fifth-place finish at last year's EuroBasket in Riga to earn a trip to the 2010 FIBA World Championship for Women in the Czech Republic.
After an impressive road win in the EuroCup Women Semi-Final first leg, Dikeoulakos spoke about the need for his players to concentrate on the little things back in Athens and said his players would be punished by Kursk if they relaxed for a second.
Kursk had hit back from an 18-point first-leg deficit to stun Municipal Targoviste in their Quarter-Final second leg.
Athinaikos had a dream start on Thursday, storming into a 19-9 lead by the end of the first quarter for a 16-point advantage on aggregate.
Dimitra Kalentzou, the point guard of the Greek national team, had six points and former Team USA center Ruth Riley contributed five.
Kursk closed the gap to five on three occasions in the second quarter but went to half-time trailing 36-26.
Kalentzou had nine points at the break.
The Greek team went in front by 13 in the third quarter but Kursk refused to give up and in the final frame chipped away.
They never had quite enough to seriously threaten Athinaikos and lost by five for an 11-point defeat on aggregate.
Riley, a mid-season signing, played like an all-star.
She finished with 17 points and nine rebounds while fellow center Irena Vizbariene of Lithuania ended up with 10 points and eight boards.
For Kursk, Donnette Snow scored 11 points and Jillian Robbins weighed in with 10 points and nine rebounds.