The result has left both teams with 5-4 records, but Sopron also have one more point because of the recent CSKA forfeit to TTT Riga.
The 19-year-old Serbian international power forward Jelena Milovanovic tore apart CSKA with 27 points and eight rebounds.
MKB also forced the Russian giants into 18 turnovers while committing just five themselves.
CSKA, who played on Sunday and beat Gambrinus in Brno, started the game ice cold and MKB took advantage by scoring the first 11 points.
The first basket for Gundars Vetra's team came four and a half minutes into the contest when Edwige Lawson-Wade sank a jump shot to reduce the arrears to 11-2.
MKB continued to battle, though, and went on a 10-4 run over the next four minutes to lead 21-6.
The first quarter set the tone for the game.
MKB got on top and stayed there, twice increasing the advantage to 16 in the second quarter after baskets from Milovanovic and Holt.
Liudmila Sapova's jumper with 39 seconds left in the frame closed the gap to 42-34 and that's how it stayed until half-time.
CSKA pulled to within six points three times in the third quarter but each time, MKB had an answer and kept their noses in front.
After Ann Wauters hit a jumper to make it 42-36, Holt replied with a three-pointer.
Wauters buried a three with 5:15 to go in the third, only for Katalin Honti to score at the other end immediately for Sopron.
Ilona Korstin's jump shot cut the gap to 53-47 with 4:25 to go in the third, but Honti's lay-up took the advantage back to eight.
Russia international Becky Hammon scored 19 points for CSKA.
Next up for Sopron is a tough away game at Gambrinus while CSKA must host Group B winners Umana Reyer Venezia.
Norbert Székely (coach MKB Euroleasing Sopron):
"Hard to say anything after a great succes like this one. Its like a dream. The team and our fans were fantastic today."
Gundars Vetra (coach CSKA Moscow):
"We hadn't enough power to stop Sopron's great rhythm. Congratulations to them, they played really well."
Honti Kata (MKB Euroleasing Sopron):
"It was really enjoyable to play in our gym tonight. Many thanks to our fans! We are very happy."
Janel McCarville (CSKA Moscow):
"Sopron started the game better. We tried to come back into the game, but Sopron seemed very strong."