The fifth-seeded Blazers (15-15) will take on fourth-seeded UCF in the conference tournament quarterfinal round on Thursday night. The Knights dealt UAB a loss in the regular-season finale on March 3.
Moore scored 22 points and pulled down 14 rebounds, while Soko finished with 20 points and had 12 boards for the Blazers, who have won five of their last six contests.
The Green Wave led 28-27 at intermission, but Moore scored the first four points of overtime to fuel a 14-7 Blazers run and they never trailed again. UAB outscored Tulane 45-36 in the second half to seal it.
Josh Davis scored 20 points to pace the 12th-seeded Green Wave (15-16), who ended their season with eight straight defeats.