Silva later scored with a powerful header in the 68th from Neymar's corner. The Serbs ended third in the group on three points, a disappointing campaign for them and their fans in Moscow after a bright opening game win against Costa Rica.
If they were entertaining, the PSG man with a coloured hair was at his usual best teasing the Serbian defence with his skill and pace on the left but wasted too many great opportunities in the end. He is a crucial part of the Brazil team, and the attacking threat he offers down the left flank is a feature of his play.
Both of Brazil's goals came when Serbia threatened to get back into the match.
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.
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Switzerland, 2-2 winners over Costa Rica finished second and will now face Denmark, who overhauled Mexico at the top of Group F on goal difference having crushed the North Americans 3-0.
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.
But Silva, the former captain who was shunned following Brazil's failure to lift the World Cup on home soil four years ago, wrapped up the win and kept hopes of an unprecedented sixth title alive.
The world most expensive player was denied at the death again by a sprawling save from Stojkovic after being picked out on the right by Jesus.
Serbia can still attempt to soak up the inevitable pressure from Brazil and hit them on the counter, or try and take advantage of set pieces with Aleksandar Mitrovic leading the way.