The 29-year-old midfielder, who replaced Jasmin Kurtic in the 72nd minute, took a Josip Ilicic pass in his stride and side-footed home a sublime shot from the edge of the penalty area two minutes later.
The result left Slovenia on four points from two games after their opening 2-2 draw in Lithuania while the Slovakians, who were beaten by England 1-0 at home, have none.
The two sides produced a largely tepid match with chances few and far between in a contest littered with ugly fouls and yellow cards at the Stozice stadium.
Slovenia keeper Jan Oblak kept out a Robert Mak sitter in the 38th minute before Roman Bezjak rattled the crossbar at the other end on the stroke of halftime.
(Writing by Zoran Milosavljevic in Belgrade; Editing by Martyn Herman)
