Biba turned on the style in the first half when she poured in 16 of her team-high 18 points to help UMMC take command at 42-25.
She has been on fire from long range, making 52.4% (11 of 21) on the season.
Latvia international Zane Tamane and Amber Holt helped Sopron stay within striking distance by scoring nine and seven points, respectively.
They trailed by 12 at the break.
Tamane would end up leading Sopron with 18 points and 13 rebounds.
There was no way to counter the depth and talent of UMMC, however.
Sopron trailed by as many as 19 points in the third quarter and 22 in the fourth.
When it was over, UMMC had five players in double figures in points.
Crystal Langhorne finished with 17, Sandrine Gruda and Maria Stepanova 16 and Cappie Pondexter 11. Gruda also had a team-high 11 rebounds.
In addition to Tamane, Sopron got 14 points and 12 boards from Angel McCoughtry.
The USA international struggled shooting the ball, though, making five of her 17 shots from the floor and missing both three-pointers.
The UMMC defense shut down Sopron, limiting them to 19 of 56 (33.9%) shooting from the field. They were one of 10 from long range in losing for the second week in a row - albeit to tough opposition.
Fener beat them last week in Istanbul, 89-72.
UMMC forward Crystal Langhorne:
"We played against a strong team, and showed good team work. We played well in defense and stopped the opponents."
UMMC Head Coach Gundars Vetra:
"Along with Fenerbahce, MKB EuroLeasing is one of the three strongest teams in Europe. We played successfully against them, because we fulfilled most of our plans and combinations. Though we've played without Celine Dumerc tonight, we played well in offense. We had a very long and hard away session. Celine was injured in Novosibirsk, she has some problems with her ankle joint, but we hope, she will join us in the game against Fenerbahce. Crystal Langhorne shined tonight, we were right to sign her. She will stay till New Year, then Candace Parker will arrive."
MKB EuroLeasing center Zane Tamane:
"We've played against one of the world's most powerful teams tonight; it's very complicated to stop them, especially on home court. Sometimes we made wrong decisions, but I'm happy, that we didn't capitulate, and tried to fight."
MKB EuroLeasing head coach Norbert Szekely:
"First of all, I want to congratulate UMMC on their win. They have a very good team - one of the strongest in Europe. I'm a great fan of this team and I'm sure they will reach the Final Four. The teams differ very much in physical strength; they made good assists, after screens and pick-and-rolls. They play very fast basketball; it was very difficult for us to play under the basket."