The Lithuanians, who had won the first leg by 14 points, triumphed again on Monday evening, taking a 69-59 victory in Stadium Arena.
Having easily passed the Swedish hurdle, Tonybet will face the winner of the Pieno Zvaigzdes and TU/Rock pair in the next round.
The visitors, who broke away in the second quarter, were led by Arvydas Siksnius who finishes the game with a team-high 26 points.
Mindaugas Lukauskis and Martynas Linkevicius added 12 and 10 points respectively.
For Dolphins, Joakim Kjellbom had a double double of 17 points and 12 boards. Jermont Horton and Pierre Hanpton collected 12 points apiece.