With rising Belgian star Hans Vanwijn pouring in 17 points, the hosts prevailed, 90-87. Aleksandsandr Zakharov had a game-high 24 points in defeat for the visitors from Russia.
Artem Komolov's two free-throws with 5:55 to go in the quarter also made it, 61-51.
Antwerp clawed their way back but weren't able to pull even and Nizhny Novgorod again pulled ahead at 76-67 early in the fourth quarter after a shot from the arc from Zakharov and his jumper.
A Vanwijn jump shot then triggered a 21-9 run to close the game for the home side. They outscored the Russia club 11-2 over the last 3:30 of the game.
The second leg will be played in Russia on Tuesday.