Nation pulled away from the precipice by Julio Cesar
Luis Felipe Scolari's side know they came too close to an exit - with much more at stake than pride - to be confident of lasting three more matches
Once the elation of victory and the hangovers wear off, Brazil will feel the cold shiver of disaster narrowly averted.
The win, after penalties, exposed the Selecao's flaws - but also their lion heart. The question now is whether that strength will be enough to paper over those weaknesses.
The abridged version of this furiously paced, draining, high-stakes match, which carried Brazil ito the quarter-finals, will read: ageing goalkeeper at the tail end of an impressive career prevents the World Cup hosts from tumbling into the abyss.
The consequences had Julio Cesar not become hero of the hour are almost too frightening to contemplate: national depression, certainly; perhaps riots, too, as the truth sunk in for Brazilians that they wouldn't win the World Cup they are paying billions for.
Little wonder that one of the first to offer congratulations was Dilma Rousseff. In this nation of 200 million people, few would have been more relieved than the Brazilian president, whose own political fortunes are in no small measure tied to the success or otherwise of the national team.
"Thank you, players" read a message on her Twitter feed.
Cesar's two penalty saves and two Chilean shots off his woodwork put the "what if Brazil loses?" question back on ice. But only for now.
So much about this victory suggested the World Cup will find out the answer to that question before the final and that the July 13 championship game most likely will not have the five-time world champions in it.
"Perhaps next time we won't be as lucky," said Brazil coach Luiz Felipe Scolari.
Cancel out Neymar - as Chile, exhaustion and the effects of a heavy first-half tackle did in the second half and 30 goalless minutes of extra time - and Brazil lose their teeth.
That was one key takeaway from Belo Horizonte. Another was that Brazil are short of a match-winning centre-forward.
Fred, ineffective again, certainly does not look the part, skying a first-half chance over the bar when he only had the Chile captain and goalkeeper Claudio Bravo to beat.
More fundamental for Brazil is that Fred was slow to anticipate, keep pace with or link up with Neymar's electric-eel attacks.
Jo came on for Fred when Scolari lost patience after 64 minutes, but he also does not look like the answer to the need for goals from players other than Neymar - who has four of Brazil's eight so far but did not score on Saturday.
Defensively, Brazil are impressive. The pairing of Thiago Silva and David Luiz is now undefeated in 17 games in which Scolari has started them together. Successive generations of thrilling forward players from Brazil have tended to overshadow some of their great defenders.
Zozimo, for instance, held the fort at the back when Brazil won their second World Cup in 1962. His story on Wikipedia is boiled down to 127 words in three short paragraphs.
Pele gets 6,000. But Silva and Luiz, who scored the first shoot-out penalty for Brazil, will not be forgotten in a hurry as the defensive bedrock of this side.
Silva, in particular, was ferocious in breaking down Chilean attacks. Their understanding failed them for Alexis Sanchez's goal for Chile that levelled the match at 1-1 on 32 minutes, a score that stayed to the end. But Luiz claimed Brazil's opening goal after Silva headed the ball toward him from Neymar's corner.
After this battering from a Chile team who would not have been undeserving winners, there is also no doubt Scolari's men have big hearts and iron wills.
So much rode on them surviving this brush with what would have been Brazil's earliest exit since 1990 from the tournament some Brazilians regard as a yardstick of their nation's and their own standing in the world.
Critics of the billions of dollars sunk into World Cup stadiums and infrastructure and the riches they suspect venal officials of creaming off would have been presented with a field day had Cesar not defied expectations.
The 34-year-old, once considered the world's top goalkeeper, looked on the verge of tears as he braced for the shoot-out. He was all smiles just minutes later.
The pressure was massive on Neymar, too, as he stepped up for what proved to be Brazil's last penalty shot.
"Neymar, Neymar, Neymar" chanted the 57,700-strong crowd, a mantra repeated across South America's largest nation, before his stuttering run ended with the ball fizzing past Bravo.
Gonzalo Jara then saw his penalty bounce off the post for Chile and Brazil exploded in celebration.
"People are demanding it from us. Because we said we would win. Now we have to give it back to them," said Scolari. "If you make a promise, you must deliver. This is what the players are doing."
But this was close, too close for a nation looking to win its first World Cup at home. Next time, this close might not be enough.