Alexandria Quigley, who once played for Sopron's Hungarian rivals MiZo Pecs, hit a three-pointer at the end of the third quarter for a 68-58 Kosice advantage.
The hosts stayed on top for the remainder of the contest, going in front by 15 before settling for an 11-point triumph.
Kosice shared the ball well, with their Serbian playmaker Miljana Bojovic particularly effective.
She finished the game with 16 points and a career-high 12 assists.
Norbert Székely's Sopron had won their opening game against Arras in Hungary so they dropped to 1-1 with the defeat.
Their guard, Shenise Johnson, is going to be a handful for opponents this year.
She ended up with 29 points, 11 rebounds and four assists.
Maroš Kováčik, Good Angels coach:
"For me it's a first victory and I really appreciate that, but to be honest I am feeling a bit confused and disenchanted. Whether we like it or not we have underestimated our opponent at the beginning and we granted them space for open shots what they managed to use and score points. They were like rolling stones and we were happy for the half time whistle. We had managed to score 46 point, but we shouldn't get 50 points against on home court - no way! I am satisfied that the girls listened to my words and I'm especially satisfied with our third quarter when we let only 9 points. We are expecting more difficult away games, and if we play in the first halves in defense like[we did] today, we could regret it."
Jelena Milovanović, UE Sopron:
"We had a chance to win today, but we didn't use it. We have to work on ourselves to get better by each game and I hope we can fix our mistakes; that will help us to play good games and reach some more wins, what means progressing into the next round."
Miljana Bojović, Good Angels:
"The most important is our victory, but we didn't start in the way we wanted and our next fault was that we didn't follow our coachs' instructions. We didn't manage to stop their main players and to play one on one defense so we worked on that a lot. On the positive side is that we started the second half more concentrated on defense, which eventually led us to victory. Offensively we were good, we scored 50 points, but in the first half main problem was defense. I think our team has strong potential so if we work hard and listen to the coach the good results will come."