Brazil goalkeeper Julio Cesar saved Mauricio Pinilla and Alexis Sanchez's attempts, while Gonzalo Jara's shot hit the post after the prequarter-final had been locked at 1-1 after extra time.
For Chile, Charles Aranguiz and Marcelo Diaz scored in the penalty shootout but it was not enough.
Chile, who were bidding to reach the quarter-finals for the first time since hosting the tournament in 1962, could have won the match in the last minute of extra-time but Pinilla's shot crashed off the crossbar.
The first game of the knockout stage was a gripping affair as both Brazil and Chile battled bravely for the normal time and extra-time but could not break the 1-1 deadlock as the game went to the penalty shoot-out.
David Luiz put Brazil ahead in the 18th minute when he kneed home after Thiago Silva flicked the ball at the near post following Neymar's corner.
Down 0-1, Chile kept the pressure on and it paid off when Brazil made a defensive error on the left, giving the ball away from a throw-in.
Alexis Sanchez made good use of the opportunity as he brought up the equaliser, sending the ball at the bottom corner, beating Thiago Silva and goalkeeper Julio Cesar on the way in the 32nd minute.
Brazil tried to hit back straight away with Neymar rising above his marker to head at goal, but the ball went wide after getting deflected on the way.
Neymar made quite a few run in the rival box and could have had a goal or two but he was always crowded out by the Chile defenders.
Chile almost scored just seconds before the halftime when Sánchez robbed the Brazilian defense and advanced into the box before slipping a pass to Charles Aranguiz but he could not steer it home as the deadlock continued.


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