Leading 50-44 at half-time, Lubor Blazek's outfit Prague outscored the visitors 27-17 in the third quarter for a double-digit lead and then pressed home the advantage in the fourth for a big triumph.
Prague are now third in Group C with a 3-5 record while Jolly JBS are fifth at 2-6.
Evanthia Maltsi hit four of six shots from three-point range on her way to 29 points to lead all scorers while Michaela Feranciková contributed 24 and also pulled down 11 rebounds.
Feranciková has been a vital part of the Prague machine this season, averaging 13.6 points and 7.8 boards, numbers that would suggest she may get a return call to play for the Czech Republic next summer at the EuroBasket Women.
Sonja Kireta made her first EuroLeague Women appearance in more than a month for Prague but didn't score.
Prague never trailed in this game but did not take the lead for good until Maltsi snapped a 29-29 tie with a three-pointer just over two minutes into the second quarter.
They went in front by 11, only to see Sibenik claw the deficit back to six points at the break.
After the restart, Feranciková and Lindsay Whalen scored on consecutive trips down the floor for a 10-point advantage and Prague were on their way to a convincing triumph.
Luca Ivankovic and Ivana Jurcevic poured in 18 and 14 points, respectively, for Jolly JBS.
Lubor Blazek (Coach ZVVZ USK Prague)
"It was a very important game for us, we needed to win by at least seven points and I'm very happy to have score more than 100 points in one game for the first time in EuroLeague. We didn't play very good defense in the first half, for two thirds of the game we weren't able to gain a bigger lead and the match was decided in the end, when we improved our defense. We are having troubles with some players, Sonja (Kireta) is still recovering, Sandra can't play for about three months, but I believe we will be able to strengthen before our match against Gdynia."
Stipe Bralic (Coach Jolly JBS Sibeník)
"We weren't able to defend well. For the whole game, USK dominated us. They were simply better and therefore they won."