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.