Bravo stopped Portugal's first three spot kicks from Ricardo Quaresma, Joao Moutinho and Nani while Chile converted their first three to win the clash of South American and European champions.
That meant that Portugal captain Cristiano Ronaldo, who usually goes last in the shootout, did not get to take a kick, as was the case when Portugal lost to Spain on penalties in the Euro 2012 semi-finals.
The result was justice for Chile after they hit the woodwork with two successive shots in the dying seconds of extra time.
Arturo Vidal struck the post and the rebound fell to Martin Rodriguez who hit the underside of the crossbar with the goal at his mercy.
There was controversy shortly before that when Chile winger Alexis Sanchez went down in the box under a Jose Fonte tackle but the referee did not consult the Video Assistant Referees (VARs), even though contact seemed to be made.
Bravo has been criticised for his club form with Manchester City this season but he was Chile's hero alongside Vidal who gave another inspired and tireless performance in midfield.
"Claudio was amazing and the penalty takers were amazing and I think we deserve to be in the final," said Chile coach Juan Antonio Pizzi. "Claudio and the goalkeeping coach had studied the penalty takers."
Chile will face either Germany or Mexico, who meet on Thursday, in Sunday's final in St Petersburg to close an exhausting two weeks.
The game only came to life in exasperating patches.
It started promisingly as Chile forward Eduardo Vargas had an excellent chance blocked by Rui Patricio, then Andre Silva's close-range effort was smothered by Bravo at the other end.
Vargas provided the high point of the second half with a brilliant overhead shot which Rui Patricio saved while Ronaldo had several second-half chances.
One effort was parried by Bravo, then he sent a long-range free kick high and wide, then had a shot deflected wide and then missed the target with a header from Cedric Soares' cross.
Sanchez was largely kept under wraps and Chile's record scorer did not have his first sniff of goal until early in extra time when his header from Mauricio Isla's cross curled away from the goal.
Portugal coach Fernando Santos pointed out that the same three players who missed on Wednesday all took penalties and converted when his side beat Poland in their Euro 2016 quarter-final. "On that occasion, they were heroes," he said.
(Writing by Brian Homewood; Editing by Toby Davis and Pritha Sarkar)
