Half-time substitute Roman Bezjak scored twice to deny the visitor the three points it required to book a play-off berth.
While the result was not enough to revive Slovenia's remote hopes of qualifying, it will sting Scotland the most given they held control over its own destiny.
Gordon Strachan's side was second in Group F coming into the match and looked on course to advance when Leigh Griffiths broke Slovenia's record of having not conceded at home this campaign.
But joy soon turned to disaster for the visiting Tartan Army as the unheralded Bezjak scored twice in the space of 20 minutes to gift Slovakia second spot behind England.
Scotland's chances flickered back to life in the closing moments when substitute Robert Snodgrass bundled in an equaliser before Bostjan's Cesar late sending off, but it was not enough to salvage an all-important victory in what could prove Strachan's final match in charge.