After impressing in his cameo against Costa Rica, Liverpool attacker Roberto Firmino could also be pushing for a starting place.
But the Brazilians broke the deadlock moments later and Philippe Coutinho was at the heart of the move as he picked out the run of Paulinho with a delightful pass over the top, and the midfielder lifted the ball over Stojkovic from 16 yards out to score.
Those misses were promptly punished in the 68th minute when Neymar sent in a corner from the left and Thiago Silva rose at the front post to beat Nikola Milenkovic to the ball and power home a header.
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. Coutinho once again came through for Brazil as he put the victor home in the 91st minute while Neymar sealed the match off with one of his own in the 97th. Brazil, with four points, will be certain to progress with a draw.
The South American giants suffered a setback in the 10th minute, however, when Marcelo was forced off with what appeared to be a foot injury, with Filipe Luis replacing him at left-back.
Mitrovic towered over right-back Fagner near the 65th minute but only to fire his header straight at Alisson with the entire goal to shoot at.
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. He then jumped above Serbia's defense from a corner for Brazil's second goal.
They had yet to click in their earlier games, where they limply drew 1-1 with Switzerland and needed two stoppage-time goals to beat Costa Rica, and they didn't exactly sparkle in the first half-hour on Wednesday.