Norway's defeat against runaway Group E leaders Switzerland earlier in the day left the fight for second place wide open and Slovenia took full advantage with goals in each half from Milivoje Novakovic (13) and Josip Ilicic (80).
The first meaningful action of the game saw Slovenia take the lead. Zlatan Ljubijankic found Novakovic with a pass from the left and the veteran striker finished low past Antonis Georgallides.
Cyprus had Georgallides to thank for keeping in touch on the half-hour mark as the keeper produced a fine stop to keep out Andraz Kirm's strike from the edge of the area out.
The hosts showed some intent at the start of the second half, and Konstantinos Makridis saw his shot blocked by Slovenia goalkeeper Samir Handanovic. There were chances at both ends as Ilicic was brilliantly denied by Georgallides, who was matched by Handanovic 15 minutes from time when he kept out Vincent Laban.
When the second goal did finally come it went to Slovenia, with Novakovic this time the creator as he set up Ilicic to finish from inside the box for a strike which killed of a spirited challenge from Cyprus.