Kevin Kampl grabbed a 19th-minute winner for the hosts to leave Albania in third place on 10 points, five adrift of group leaders Switzerland with three games to play.
Slovenia stayed fifth on nine, but still have a slim chance of finishing second and grabbing a spot in the play-offs.
After a positive start, Slovenia took the lead when Kampl fired home with a rasping drive from distance that flew into the top corner.
Albania pushed forward in the second half and Slovenia goalkeeper Samir Handanovic was called into action to deny a close-range effort from Lorik Cana and a strike from outside the box by Hamdi Salihi.
Albania travel to Iceland on Tuesday and Slovenia visit Cyprus.
- Sports & Recreation