A titanic second-round battle in Belo Horizonte saw Brazil beat Chile 3-2 on penalties after the South American rivals finished extra time locked at 1-1.
The penalty drama unfolded after a pulsating game at the Mineirao Stadium which saw Chile almost snatch victory in the closing minutes of extra-time when substitute Mauricio Pinilla's shot crashed back off the woodwork.
"If you don't exploit the few opportunities you get, you can go out," relieved Brazil coach Luiz Felipe Scolari said afterwards.
"We almost paid the price in the 118th minute when the ball hit the bar."
Brazil, roared on by their partisan support, started strongly, taking the lead through a goal credited to David Luiz after 18 minutes.
Neymar swung a corner in from the left and the Paris Saint-Germain defender rose to turn the ball into the net.
But Chile came back and equalised after 32 minutes, Barcelona star Alexis Sanchez punishing slack play in the penalty area to slot past Cesar.
In the shoot-out, both teams missed spot-kicks to leave Neymar as Brazil's fifth and final penalty-taker.
The Brazilian poster-boy duly tucked away his penalty to make it 3-2 and when Jara missed, the hosts celebrated.
- Hero Cesar -
Brazil's goalkeeping hero Cesar had broken down in tears just before the shoot-out, highlighting the excruciating tension of the moment.
"The Brazilian people needed this, and so did the players. We knew how difficult it would be," said Cesar.
"I hope that our coming matches don't go to penalties, because otherwise our families will end up having heart problems."
The Brazilians will now play Colombia in the quarter-finals in Fortaleza on Friday after 22-year-old Rodriguez served up a two-goal display in a 2-0 win over a Luis Suarez-less Uruguay at the Maracana.
Rodriguez produced a moment of genius after 28 minutes which is likely to be a strong contender for goal of the tournament.
Collecting the ball on his chest with his back to goal, the Monaco youngster swivelled and uncorked a dipping volley which flew in off the bar.
His second was a simple tap-in after Juan Cuadrado headed Pablo Armero's deep cross back into the danger zone.
The win puts Colombia into the quarter-finals of the World Cup for the first time -- and shot Rodriguez to the top of the tournament goalscoring charts with five goals from four games.
The build-up to the match had been dominated by the biting controversy surrounding Suarez which saw Uruguay's talisman sent home in disgrace and banned for four months.
Even though Suarez was back home in Uruguay, his team laid out his kit in the changing rooms at the Maracana.
But Uruguay dearly missed his presence as they were dominated by the skilful Colombians, who have emerged as one of the most exciting teams in the tournament.
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- James Rodriguez