The victory, and Switzerland's 2-2 draw with Costa Rica, meant Brazil finished top of Group E on seven points, two ahead of the Swiss who will face Sweden in the last 16.
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For Serbia, Mitrovic was a direct force up front, while Tadic picked up where he left off against Switzerland, being a threat down the right.
Despite the loss of Real Madrid full-back, the Brazilians continued to push forward and they went close to scoring on 25 minutes but Vladimir Stojkovic produced a good save to deny Neymar from close range.
Tite's team went into the game knowing a draw would be enough to see them through, while the Serbs needed a win to guarantee progression for them to the last 16 in Russian Federation.
Brazil had an early setback when left back Marcelo was substituted in the 10th minute, limping off the field.
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The pressure is a little bit gone but on the other hand you want to have a good feeling going into the next round. As a result he has become the first player since Diego Maradona to accomplish such a feat in the World Cup .
Neymar forced a first save from Stojkovic in the 25th minute but the Serb keeper did well to palm his hopeful effort wide of the goal.
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 gave his team the lead when he met a lofted ball from Philippe Coutinho in the 36th minute. A Seleção dictated the pace of this game for large parts, although it should also be acknowledged that they were under major pressure when Thiago Silva popped up to head home that decisive second goal.
This will be the second meeting between Serbia and Brazil with the former as an independent nation - their first encounter was in a friendly in June 2014, Brazil winning 1-0.
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.