Having unexpectedly won on the road at Schio, the Good Angels pressed home that advantage with a hard fought 65-59 home court win.
It had looked like the Italian visitors might extract some sweet revenge in the early stages after they silenced the home crowd with an 18-13 lead but a disastrous second quarter proved costly.
The Good Angels came storming back and produced a blistering second quarter display outscoring Beretta-Famila 26-15 to head into the interval 39-33 in front.
It was all too comfortable for the home side in the third period and they stretched their lead to 54-43 but they then had to really work for their win.
A 9-2 start by Schio got them back into the contest and home nerves were jangling as the Italians got to within one shot at 60-57 with just over 90 seconds remaining.
However an unsportsmalike foul on Elisabetta Moro swung the momentum back to Kosice and they kept their cool from the line to seal a famous victory.
The loss was tough on center Mudju Ngoyisa who claimed an impressive double-double of 18 points and 12 rebounds but a sloppy 25 turnovers sealed the fate of Schio.
Candice Dupree and Angel McCoughtry combined for 27 points for Kosice but it was Miljana Musovic also reaching double digits that made a big difference.
Stefan Svitek, Good Angels Kosice coach:
"It was a very tough match mentally and that's why there were too many turnovers and missed shots. Our opponents tried hard in the first half and we were behind. In the second half we built a decisive edge. I am happy that we achieved such a success right in front of our fantastic audience."
Alena Kovacova, Good Angels Kosice player:
"Most playoff games are full of nerves, one needs to put everything into the game. We did so tonight, we were on top of our opponent and we were better physically. We wanted this victory very much. We are enjoying ourselves and looking forward to the next challenge."