Berti Vogts' Scotland failed to silence their critics with a nervous and frustrating goalless opening to their World Cup qualifying campaign.
Goalkeeper Borut Mavric's superb save prevented a Paul Dickov chip giving Scotland an early lead in a first half dominated by the home side.
But Craig Gordon was lucky to survive after colliding with Malky Mackay and also letting slip a Nastja Ceh drive.
Slovenia had better chances, but Mavric saved well to deny Nigel Quashie.
The visitors had stuck by the side that opened their campaign with a 3-0 win over Moldova.
Steven Pressley had failed a late fitness test, so Scotland manager Vogts made one change from the side that drew in Spain, Dickov replacing Stevie Crawford up front.
Dickov almost made a whirlwind start, latching on to a James McFadden header, but the striker's toe poke was tipped on to the bar by Mavric at full stretch.
Mavric's punch from the resulting corner would have headed into his own net if it had not been for a goal-line clearance from Jalen Pokorn.
Slovenia settled after the opening 10 minutes and threatened when Milenko Acimovic's free kick from 22 yards struck the head of Jackie McNamara and flew a couple of feet over the bar.
Gary Naysmith surged into the Slovenian box but saw his low drive from 12 yards deflected across the face of the goal and out for a corner.
McFadden was next to threaten, his superb curling effort from 20 yards drifting a foot wide of the far post.
Gordon stood up well at the other end to a powerful effort from just inside the box from Ermin Siljak, punching the ball off his line.
Scotland rode their luck early in the second half when Gordon collided with Mackay while going for a cross from Ceh.
The goalkeeper dropped the ball at the feet of Siljak, but the striker's shot struck the head of Mackay as it headed for the unguarded net.
Ceh then held off Mackay and played the ball into the path of Acimovic, who ought to have done better than hammer the ball over from 16 yards.
Midfielder Ceh tried a speculative 25-yard drive that was spilled by Gordon, but the Hearts goalkeeper grabbed the ball before it crossed the line.
Scotland did threaten late on, Quashie stinging the fingertips of Mavric with a rasping 22-yard drive that the goalkeeper turned over the bar.
Scotland: Gordon, Caldwell, Webster, Mackay, Naysmith (Holt 59), Fletcher, Ferguson, McNamara, Quashie, Dickov (Crawford 80), McFadden.
Subs Not Used: Marshall, Miller, Cameron, Pearson, Anderson.
Booked: Dickov, McFadden.
Slovenia: B Mavric, Karic, Knavs, M Mavric, Pokorn, Seslar, Ceh, Komac, Dedic (Sukalo 79), Siljak (Lavric 64), Acimovic.
Subs Not Used: Handanovic, Tanjic, Cesar, Koren, Ilic.
Booked: Seslar, Karic, Knavs.
Referee: Claus Bo-Larsen (Denmark).