He also got his glove to a Vinicius Junior strike, which Richarlison turned in on the rebound from close range.
The goal of the tournament came soon after, an acrobatic bicycle kick after flicking up a Vinicius cross from the left, giving Milinkovic-Savic no chance.
Dusan Vlahovic came off the bench for Serbia, but the Juventus striker was still visibly not fully fit with that recurring groin inflammation.
However, Brazil were worried because Neymar went off injured in the second half after badly spraining his ankle under a Milenkovic tackle.
He was pictured in tears sitting on the bench as medics wrapped an ice pack around the ankle.