Juventus started the game well and finished the first quarter with a 16-13 advantage, increasing the gap to 38-32 at the halftime break.
However, the six-point edge on the evening and a nine-point advantage on aggregate disappeared in the third quarter, as Tonybet took a 56-53 lead heading into the final period.
The hosts began the fourth quarter with an 8-0 run, with six points coming from Vaidas Cepukaitis. Prienai led by as many as 15 points in the period and convincingly advanced to the next stage.
Zygimantas Janavicius led Tonybet with 16 points, while Mindaugas Lukauskis and Gintaras Kadziulis added 14 points apiece.
For Juventus, AJ Matthews scored a team-high 16 points and grabbed eight rebounds, as Nikita Barinov added 13 points in a losing effort.