After rolling to a 68-48 win in France, Kursk returned home to Russia and prevailed 72-51 for a 140-99 triumph on aggregate.
Varvara Psareva was among Dynamo's leading players in the second leg with 11 points and 11 rebounds but she was ejected from the game in the second half.
They out-rebounded Mondeville 57-28 in the game.
Athinaikos BC were 90-72 winners over SK Cesis in Greece. The second-leg success gave the hosts a 158-129 win overall.
Athinaikos made sure there would be no comeback after the first meeting, opening the game by outscoring SK Cesis 26-11 in the first 10 minutes.
Kathryn Ann Gearlds had 23 points for Athinaikos BC.
Elitzur Ramla stormed into the next phase with a 67-62 victory over Olivais Coimbra.
Nkolika Nonyelum Anosike had 16 rebounds to go with her 12 points for Elitzur, who won the tie 144-122 on aggregate.CB Feve San Jose clinched their passage to the next phase of the play-offs with an 81-68 victory over Botas Spor.