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.
Pedro Martinez, Cajasol coach:
"I am very happy with how we played in defense and how we started the game agressively. And that decided the result of the whole game. We didn't expect such an easy game, especially after the Energa Czarni performance in Sevilla. But we didn't expect the fans to cheer for us, it helped us win the game."
Michal Ignerski, Cajasol player:
"Our defense is still not what we would like to see, because we haven't been ong with our [new] coach."
Gasper Okorn, Energa Czarni coach:
"I apologize to everybody for what happened today. It has never happened in my career before. I cannot put in words what I feel now. The problem is not that we lost, but how we looked today and in the past few games. I will not run away from responsibility, so tomorrow I will talk to the board of the club and I shall put my head on the plate."