Zlatko Dedic put them in front after 12 minutes in Maribor and Milivoje Novakovic added a second on the stroke of half-time before Valter Birsa put the match beyond reach of Poland.
Dedic was at the centre of controversy early in the match when he was booked for diving in the Polish penalty area in the tenth minute but three minutes later he became the hero.
Miso Brecko did some good work down the right and Dedic was on hand to shoot home right-footed from his cross for his second international goal.
The half was largely uneventful from that point until the final minute when Dedic laid on Slovenia's second. He picked out Andraz Kirm and he crossed from the right-hand side of the penalty area to the unmarked Novakovic, who made no mistake.
The game was all over after 62 minutes when Novakovic and Kirm combined well before the ball reached Birsa on the left wing and he was able to advance on goal and put the ball beyond Poland goalkeeper Artur Boruc.