|Sophia Young had 27 points|
Trailing by 12 points after last week's clash in Italy, Galatasaray returned to Istanbul and prevailed 82-61 for a 137-128 triumph on aggregate.
Galatasaray also hit back from a 14-point first-leg deficit in their Semi-Final triumph over Dynamo Kursk.
Taranto, despite being outplayed on Thursday night, had a chance to win at the end of regulation after two Marina Kress free-throws had given Gala a 69-57 advantage with 34 seconds left in the second leg.
Those two shots from the charity stripe tied the contest on aggregate.
Roberto Ricchini's team went to the other end looking for the winner but ex-France international Audret Sauret-Gillespie turned the ball over, giving the Turkish giants a chance to win the EuroCup at the death.
They held the ball until the waning seconds but Seimone Augustus, who had 23 points in the game, was off target with a jump shot.
|Seimone Delicia Augustus (Galatasaray )|
After the teams exchanged baskets at the start of overtime, an Augustus jumper and a Young three-ball gave Gala a five-point advantage on aggregate and they stayed in front the rest of the way.
The home side ended up outscoring Cras 13-4 over the final 10 minutes.
Young poured in a game-high 27 points for Galatasaray.
Megan Mahoney finished with 20 for the visitors.
In the second leg, Galatasaray out-rebounded Taranto 43-23. The hosts did a lot of damage at the free-throw line, making 17 of 23 compared to six of seven for the Italians.