The result left Slovakia second in the standings with 15 points from seven games, two behind leaders England who stayed in the driving seat for automatic qualification with a 4-0 victory in Malta.
Scotland moved one place up to third on 11 points after a 3-0 win in Lithuania, ahead of Slovenia on goal difference with both teams still in with a slim chance of reaching next year's tournament in Russia.
Slovenia goalkeeper Jan Oblak made six vital saves in the first half, keeping out two stinging shots apiece from Marek Hamsik and Robert Mak while he also parried a pair of close-range sitters by Nemec.
Mak shot just wide of the far post shortly after the break as the visitors continued to soak up pressure and the home side showed continued profligacy in front of goal.
Their adventurous 4-3-3 formation, akin to the one that impressed in the 2010 World Cup in South Africa when they reached the last 16, was finally rewarded in the 81st minute.
Livewire Mak broke down the right, yet again, and squared the ball into the five-yard box for Hamsik to hit the underside of the bar and Nemec bundled in the rebound for his fourth international goal in as many games.
The nine group winners in Europe will qualify automatically for the 32-team event, while the eight best runners-up enter a two-leg playoff for an additional four berths.
(Writing by Zoran Milosavljevic; Editing by Christian Radnedge)
