ZKK Crvena Zvezda led by as many as 17 points before settling for an 82-73 triumph at CSB CST Alexandria.
The home side showed great resolve and trimmed the deficit back to six late in the game, only for Tanja Miranovic to bury a three right at the end to give the visitors a nine-point advantage heading into the second leg.
Iva Roglic had 19 points, seven rebounds and four assists for the winners.
Tiffany Porter-Talbert had 14 points and 11 boards in defeat.
In Banja Luka, Bosnia and Herzegovina, Mladi Krajisnik won 83-77 over AKO Aris Holargou.
In a thrilling contest, the hosts Mladi Krajisnik only led 78-77 with 50 seconds remaining but scored the last five points of the game and that could be crucial when the second leg is played.
Dragoslava Zakula had 22 points and Aida Pilav 17 in the victory.
Gran Canaria claimed an 80-62 triumph at the Flying Foxes to take a stranglehold on their tie.
Tiina Sten had 15 points and Naomi Halman 13 for the Spanish outfit.