After 120 goalless minutes a shootout was required to separate the two sides, with the South American champions thumping the reigning European kings.
Manchester City keeper Claudio Bravo was the hero, keeping out all three of the Selecao's spot kicks to help his side through to the final, where they will face either Germany or Mexico on Sunday.
Neither side could do enough to find a way through in normal time, with the first chance falling the way of Eduardo Vargas after being played through by Sanchez.
It was proving to be an open contest, as both Andre Gomes and Silva again came close for the Selecao either side of some Chile pressure.
The chances were continuing to arrive in Kazin but both teams failed to make the most of them - Vargas seeing a flying volley kept out by Patricio and Cristiano Ronaldo coming out second best against Bravo from a tight angle.
Chile, ranked four places higher than their opponents in the latest FIFA rankings, continued to let fly as both Vidal and Sanchez failed to find the intended target from range.
As the 70-minute mark approached the sides had mustered 10 shots apiece, but the writing was on the wall when Ronaldo headed wide from seven yards out.
Chile were on top in extra time and should have won it through Sanchez, who failed to convert inside the box to leave him stuck on 31 goals for the season.
There was some drama to come in the second half of extra time after substitute Francisco Silva knocked the ball past Jose Fonte and was brought down, though the referee decided against using the video assistant and did not award a penalty.
Vidal then hit the post with his strike from the edge of the box, before Martin Rodriguez hooked it against the crossbar from the follow-up, but it would matter little in the end as La Roja held their nerve from the spot.