Having opened his Russian Federation 2018 account with the second of Brazil's two late goals in Friday's 2-0 win over Costa Rica, Neymar was again impressive.
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'm apparently at peace", the Brazil coach said.
As Group E winners, Brazil will now face Mexico in Samara on Monday, with group runners-up Switzerland taking on Sweden in St. Petersburg on Tuesday.
Serbia needed to win to qualify and rocked their opponents with a flurry of second-half chances.
Playing hours after holders Germany suffered their shock exit after a 2-0 defeat by South Korea, Brazil were desperate to stamp their authority on a tournament where World Cup pedigree has counted for so little.
England hat-trick hero Kane basks in World Cup rout
It wasn't Kane on the end this time but Stones, who was left unmarked to score his first worldwide goal. Kane made it five just before the break after he had been wrestled to the ground.
Brazil eliminated Serbia and secured their place in the second round of the World Cup after a comfortable 2-0 victory in Moscow.
Philippe Coutinho skips out of the tackle from Nemanja Matic during Brazil's 2-0 win over Serbia.
Silva popped up just at the right time for Brazil, and not only in defense.
The Brazilians have not hit top gear going forward yet, although they are a better organized and steelier prospect under Tite than they were four years ago, and have shown they can mix the mundane with the sublime.
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.
That gave Brazil the breathing space they craved, and they noticeably relaxed with the two-goal cushion as Serbia ran out of ideas and steam.