Victory against Serbia will see them progress as group winners but defeat, coupled with a Switzerland win against Costa Rica - could see the five-time winners leaving the tournament prematurely.
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.
The World Cup match between Serbia and Brazil will be broadcast live on Fox.
Aleksandar Mitrovic is hoping the fear of failure will pile the pressure on Brazil and provide Serbia with a route through to the World Cup knockout stages.
The Serbs almost scored in the 61st when Brazil goalkeeper Alisson pushed the ball into the path of forward Aleksandar Mitrovic, whose shot bounced off the keeper and was bound for goal before being cleared by Silva. "We had chances to equalize, but we missed our chances and we were punished". Brazil only need a draw to go through, but will be eyeing first place with a win.
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Brazil had an early setback when left back Marcelo was substituted in the 10th minute, limping off the field.
This was a more assured performance from Brazil compared to its first two group matches.
Jesus' extra touch robbed the Manchester City striker of a clear chance near the half-hour mark - his delayed right-footed shot from just outside the six-yard box hitting a recovering defender after running in behind the back line.
Antonio Rukavina, who started in place of the experienced Branislav Ivanovic, saw his shot pushed into the danger area by Alisson and the goalkeeper was relieved to see Silva stop Mitrovic nodding the loose ball home.
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.