The win improved the Seville outfit to 2-2 in Group A while dropping the Slupsk club to 1-3.
The visitors' run that the Poles never recovered from came at the start of the second quarter.
After Jason Straight's three-ball had cut the deficit to 15-12, a Mile Ilic three-point play sparked an 11-0 scoring burst for Cajasol.
Dusko Savanovic had a three-pointer in the run, and he closed it with a three-point play as Cajasol led 26-12.
Cajasol stepped on the accelerator and opened up a 43-19 lead late in the second quarter and pulled away for a big win.
Niklas Medley poured in 22 points for the winners.
American Medley, playing in just his second EuroChallenge game, missed only one of two shots from three-point range but everything else went in as he finished 10 of 11 from the floor and a perfect one of one at the charity stripe.
Cajasol out-rebounded Energa Czarni 41-32.