The resilient Poles got a three-pointer from Ivana Matovic with 26 seconds left in regulation to tie the game and force overtime, and then beat Jolly JBS 79-72 in the extra period.
Matovic was outstanding, pouring in 25 points in the game.
The lead went back and forth in the final quarter but the Croatian outfit took the upper hand at 68-63 with 1:10 left after Constance Jinks made one of two at the free throw line.
That miss proved costly.
With 59 seconds to play, Sibenik fouled Monique Curry and the American made both at the stripe to close the gap to three before Matovic tied the contest with her three-pointer.
Jolly JBS called a timeout and when play resumed, they ran the clock down to 10 seconds before Ivana Jurcevic launched a three but she was off target.
Curry rebounded and Lotos PKO BP's Natallia Marchanka put up a potential game-winning shot from behind the arc but also missed and the game went to overtime.
Marchanka opened the extra period with a three and her fellow Belarus international Katsiaryna Snytsina followed with a basket as Lotos PKO BP went in front by five.
Alana Beard then made two free throws to extend the advantage to 75-68 for the Polish team with 3:26 to go.
Jolly JBS closed the gap to three with 1:43 remaining after a Jinx basket but Snytsina replied with a jumper and Matovic finished off the scoring with a jump shot.