The Selecao's clash with Jorge Sampaoli's side was level at 1-1 after 120 minutes of action, leaving a place in the quarter-finals decided by a penalty shootout.
With the scores tied at 2-2, Neymar took his side's fifth spot kick and calmly found the net while Chile's Gonzalo Jara was denied by the post to send Scolari's men through into the last eight.
Scolari told reporters: "Neymar is 22 but he has the experience of a 35-year-old. Psychologically and mentally, he is very prepared."
Brazil will face Colombia in their quarter-final clash next week.