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.
"I never like to speak about myself, it is not something that goes through my head", he told reporters at Brazil's base camp last week.
Brazil finished first in Group E and will next face Mexico in the round of 16 on Monday in Samara.
The selecao left their last match against Costa Rica late, but eventually put two past Keylor Navas in stoppage time to get the win. Serbia ended third on three points and are eliminated along with Costa Rica.
Tite's side probed away at the White Eagles in the first half before Paulinho made the breakthrough in the 36th minute to give them a 1-0 lead at the break.
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Needing to avoid a loss to be sure of advancing, Brazil fielded the same XI as their 2-0 win against Costa Rica as Tite looked for improved understanding among his starters.
Silva popped up just at the right time for Brazil, and not only in defense. But Brazil broke swiftly from the ensuing corner and Coutinho played in Neymar who was denied again by Stojkovic.
Mitrovic then headed straight at Alisson when he found himself free in the box, as Serbia failed to land the telling blow with Brazil rocking.
After Miranda had nearly steered an Adem Ljajic ball into his own net, Aleksandar Mitrovic missed with two headers, the first striking Thiago Silva after Alisson's flap and the second straight at the goalkeeper from close range.
Four years ago, Paulinho was part of the Brazil team that was humiliated at home in a 7-1 drubbing by Germany in the semifinals.
"We were on the front foot in the first half except for the moment when Brazil scored", said a somewhat optimistic Serbia coach Mladen Krstajic.