The host nation won the shootout 3-2, however, with Neymar scoring what proved to be the winning penalty.
Here, Sports Mole dissects what was an incredible last-16 clash between the two South American rivals.
On target: 13
On target: 5
Was the result fair?
In truth, fairness goes out the window in penalty shootouts. It was all about who could handle the pressure and ultimately the deafening home support was enough to carry Brazil over the line. The Selecao have their name in the last eight of the tournament, but Chile can be proud of their performance, not just today, but in the tournament as a whole.
The first 45 minutes was the most explosive half of football in this summer's World Cup, with the two teams rightly on terms at the break. It was Brazil that looked the most likely to win it late on and indeed in extra time, but Chile were so well-drilled that Luiz Felipe Scolari's side could not find a way through.
Both teams put so much into the occasion that it was always going to be difficult for the loser to take, but Brazil managed to edge through. Taking the fixture as a whole, the home side perhaps just about deserved to advance.
It would be fair to say that Brazil underwhelmed in the group stages despite topping Group A, but they produced their best performance of the competition this afternoon. The Selecao started on the front foot and deserved to take the lead after 18 minutes, but they continued to look shaky in defensive areas, with Sanchez capitalising on some poor play from Hulk and Marcelo.
In truth, if Brazil had an expert finisher in attack then they might have secured victory in normal time. However, Fred and indeed his replacement Jo both passed up strong opportunities. Scolari's side were impressive in the first period, but a number of their influential players - Neymar included - struggled to make an impact in the second 45 minutes.
That said, Brazil must be praised for their ability to deal with the immense pressure. Chile were seen as serious dark horses for this tournament, but Brazil showed that they have the heart to go with their talented squad.
On the face of it, a last-16 exit this summer could be seen as a disappointment for Chile. However, it was anything but. The South American outfit came through a group that included Spain and Netherlands, while they took the host nation to penalties this afternoon.
For long spells, Brazil really struggled against Chile's high pressing and movement in attack and, on another day, they would have sent Brazilian football supporters into meltdown by eliminating the hosts from the tournament. Sanchez and Arturo Vidal were both terrific for Chile, while a patched-up Gary Medel also starred in defensive areas. Brazil did look the side most likely to win it as the match advanced, however, with Chile struggling to keep 11 players on the field due to a number of bumps and bruises.
The South American side showed incredible mental strength to stay in the match even when they were struggling as the match headed for penalties. They got off to a difficult start in the shootout - missing their first two - but recovered to level at 2-2. Unfortunately, Gonzalo Jara was the fall guy after hitting the post, but Chile can leave this summer knowing that they heavily contributed to what has been an incredible World Cup.
Sports Mole's man of the match
Alexis Sanchez: If there was one player that did not deserve to be on the losing side this evening, it was Chile's Sanchez. The attacker is expected to leave Barcelona this summer and on this performance, he will not be short of offers. Sanchez levelled for Chile just past the 30-minute mark with a fine finish, while his pace and movement continued to cause problems for Brazil throughout the fixture. The former Udinese winger did miss in the shootout, but it took nothing away from his overall performance. While his teammates were out on their feet late on, Sanchez was still full of energy.
In truth, it is difficult to pick out one moment. However, Brazil's slack defending in the build-up to Chile's equaliser was poor. Marcelo found Hulk with a throw, but the attacker's touch was poor. Eduardo Vargas was quickly on the scene to pick Hulk's pocket and release Sanchez, who found the bottom corner. It was a goal that could have been avoided.
It was an eventful fixture for Howard Webb to referee. The Englishman awarded Chile two bookings in the first period despite a number of late challenges from Brazilian players, but he did turn down what looked a clear penalty for Brazil when Hulk was bundled over inside the area by Mauricio Isla.
The most controversial moment arrived in the second half, however, when Webb, along with his linesman, disallowed a Hulk goal for handball. Replays have shown that it might have brushed the arm of the attacker, but it was a seriously brave call for Webb to make from the angle which he was placed. Due to the end-to-end nature of the contest and amount of late challenges, it was a really difficult 120 minutes for the experienced official.
Brazil: The Selecao will face either Uruguay or Colombia in the quarter-finals of the competition.
Chile: Chile currently have no confirmed fixtures on their schedule.