Serbia will face off against Brazil at Spartak Stadium-Otkritie Arena in Moscow on Wednesday, June 27 at 2 p.m. ET, airing on FOX.
Paulinho scored the victor in the first half, and Thiago Silva scored in the second to set up a date with Mexico in the round of 16. Serbia ended in third place on three points and are eliminated along with Costa Rica.
The goal put Brazil back on top of their group, Switzerland having earlier gone ahead against Costa Rica, and left Serbia with an uphill task going into the second half.
Brazil struggled in their opening two matches, first held to a 1-1 draw and then needing late goals to win the other.
Paulinho made up for Brazil's faulty finishing in the 36th minute - the marauding midfielder latching onto a perfectly-lobbed Philippe Coutinho pass before poking past a charging Stojkovic and giving Brazil an earned advantage.
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Neymar was again well shackled and unable to impose himself, with one dipping shot over the bar and another at the legs of Stojkovic after a lightning counter-attack his only notable contributions in the first hour.
Both of Brazil's goals came when Serbia threatened to get back into the match.
Sure enough, Brazil regrouped and found the second when Thiago Silva headed in at the front post from a corner on 68 minutes - despite protestations from Serbia that Miranda had maneuvered Mitrovic out of the way in the build-up.
Serbia needs to pull off a big result against Brazil if the European side is to reach the round of sixteen for the first time as an independent nation. It's always hard to play against such team as Brazil, they played well.
Neymar was unlucky not to score 12 minutes after the restart - the excellent Coutinho finding the Paris Saint-Germain man racing behind the Serbia defence only to see his left-footed shot blocked by a quick-reacting Stojkovic.