Bravo saved efforts from Ricardo Quaresma, Joao Moutinho and Nani as Chile converted all their spot-kicks.
It was perhaps justice for Chile, who had a strong claim for a penalty denied deep in extra time and also hit the post twice in quick succession.
Arturo Vidal, whose shot hit the post in closing stages of extra-time before Martin Rodriguez’s follow up also hit the woodwork, was successful from the spot for Chile along with Charles Aranguiz and Arsenal forward Alexis Sanchez.
The dramatic finale lit up an otherwise dull encounter, with both sides looking tired after playing their fourth game in just 10 days at the tournament in Russia.
Portugal will play either Germany or Mexico — who face-off tonight — in Sunday’s final in St Petersburg.
Germany boss Joachim Low is thrilled with the progress his young squad have made.
Low will be seeking a 101st victory in his 151st game in charge of Germany when they face Mexico in Sochi, and believes his team have already excelled by reaching the last four in Russia.
“I’m really happy to be in the semi-final with this side,” Low said. “Our main aim is always to be one of the last four teams in any competition. And you couldn’t necessarily expect that from this team.
“Nonetheless, they did it, and did so by overcoming a few different hurdles in the tournament.
“It’s nice that the team is bonding, because the players are spending time with each other off the pitch too.
“They’re incredibly happy to be here. Not a single player is seeking to be in the spotlight — instead they all want to succeed as a team.
“We’re pleased to have made it to the semi-final and we’ll be coming up against strong opponents in the form of Mexico. We want to make it to the final. Our players are hungry, but we need to play better than we did in the first half against Cameroon (a 3-1 win on Sunday).”
Mexico coach Juan Carlos Osorio dismissed the fact that Germany’s youthful exuberance could be advantageous.
He said: “You can be young and have a lot of experience. A 30-year-old person that starts studying cardiology will know a lot less than a 21-year-old graduate.”
Bayer Leverkusen striker Javier Hernandez added: “We know about the things that could make them suffer but we are going to focus in our team and our tactics.”
Rui Patricio, Cedric, Fonte, Bruno Alves, Eliseu, Bernardo Silva (Quaresma 83), William Carvalho, Adrien Silva (Joao Moutinho 101), Andre Gomes (Gelson Martins 116), Ronaldo, Andre Silva (Nani 76).
Bravo, Isla (Fuenzalida 120), Medel, Jara, Beausejour, Aranguiz, Marcelo Diaz, Hernandez (Silva 112), Vargas (Rodriguez 86), Vidal, Sanchez.
Alireza Faghani (Iran).