Olexandra Gorbunova, who led Division A in scoring last year at 20.9 points per game, poured in 22 and also corralled 11 rebounds as Ukraine won the Group A clash, 81-76.
Iryna Biryuk contributed 16 points and Ol'ga Dubrovina 10 for the winners, who are coached by Volodymyr Bryukhovetskiy.
Noel Monik Kuin scored 19 and Gergana Branzova-Erdenay 18 for Bulgaria.
Ukraine narrowly missed out on direct qualification for the EuroBasket Women with five wins and three defeats while the Bulgarians were 2-4.
When Zornitza Kostova drilled a jump shot to put the hosts into a 36-24 lead in the second quarter, they looked to be in trouble.
At half-time, Gergana Slavcheva had 15 points for Bulgaria who were still on top at 45-38 and another three-ball from Kostova early in the second half stretched the home side's lead to 52-42.
Ukraine made their move midway through the third quarter.
Behind 56-48 after a Kuin free throw, Tetyana Shchypakina made two at the charity stripe for Ukraine and followed that up with a three-pointer to spark the visitors into life.
Bryukhovetskiy's team went on to outscore Bulgaria 19-3 over the final 4:40 of the period for a 67-59 advantage and they stayed in front for the entire fourth quarter.
Ukraine outrebounded Bulgaria 42-34.
Lyubov Alyoshkina and Olena Zherzherunova each finished with nine points and nine rebounds for the winners.
Nikolay Boroukov, head coach of Bulgaria:
"Ukraine are a great team. We had eight new players and little time to built our game in offense and in defense, a mere four days. We tried, but at the end of the game the girls were tired. We made a lot of mistakes in the third quarter and lost the rebounds.
It was because some of the players were tired by playing very aggressive in defense in the first half. Ukraine has a great experience, and it is hard to play against such big players. We will have a lot of problems in Ukraine, because they will be more relaxed. It won't be easy in Germany too, but we will do our best, because we still have our chances."