Ana Baletic, who plays for the Bosnia and Herzegovina outfit Zeljeznicar, had a season-high 23 points and nine rebounds.
With 2:57 remaining, the visitors from Serbia led 67-60.
Baletic had a pair of free throws and a basket as her team enjoyed a strong finish.
The 24-year-old forward made all 12 of his her shots from the free-throw line.
Hemofarm center Dara Kovacevic had 10 points and finished a rebound shy of a double-double.
The second leg will be played on January 14 in Vrsac, Serbia.