The home nation, ranked 93rd in the world, were second best during the first half tonight against their opposition, who had twice as many shots as Magnus Pehrsson's side.
The first concrete effort of the night fell to the Baltic state, as Ragnar Klavan's header was blocked from close range.
From then on, however, it was mostly one-way traffic, Slovenia coming forward time and time again.
The game became scrappy towards the latter stages, with Ilja Antonov of the home side and Dalibor Stevanovic of the visitors delaying the game due to injuries.
For all of Slovenia's chances, they were unable to capitalise, and so both sides went in level at the break.