The Slovakian giants improved to 5-3 in Group D of EuroLeague Women while Schio club Beretta Famila slumped to 1-7.
With 4:41 remaining in the second quarter, struggling Beretta Famila led their hosts 27-26 after Allison Feaster-Strong made a jump shot to increase her points haul to 14.
Kosice outscored the Italian outfit 14-2 for the remainder of the period to take a 40-29 advantage to the break.
Sandro Orlando's team got no closer than nine until the final minute of the fourth quarter when they shaved the deficit to six.
By then it was too late to seriously threaten Stefan Svitek's team.
Cathrine Kraayeveld, Liron Cohen and Anna Jurcenkova each had 19 points and Daniela Cikosova contributed 17 for Broker Kosice who are without their German star Linda Frohlich.
Kraayeveld also pulled down a game-high 10 rebounds.
Feaster-Strong led all scorers with 22 points in defeat.