"We are satisfied with the result and how we played but we have still not won anything," said Bravo after his heroics in Kazan.
Both Bravo and his Portugal counterpart Rui Patricio were in action just after the start. With just six minutes gone, Sanchez split open the Portugal defence with a pass for Eduardo Vargas but Patricio was alert and blocked the shot.
At the other end seconds later, Cristiano Ronaldo's cross set up Andre Silva but Bravo smothered his effort. Aranguiz twice also went close with efforts.
But, despite the goalmouth incidents, neither side managed the breakthrough and the sem-final moved into extra time.
Chile almost clinched the tie in the dying stages when both Vidal and substitute Martin Rodriguez hit the woodwork. They also had an appeal for a penalty turned down when substitute Francisco Silva appeared to be fouled by Jose Fonte.
"I'm very proud of this team," said Chile coach Juan Antonio Pizzi. "Claudio pulled off some good saves to keep us in the game. And then he had the ability to foresee where their players would put their kicks."
In the final on Sunday in St Petersburg, Chile will play the winners of Thursday night's match in Sochi between Germany and Mexico.
"It doesn't matter who we get," added Pizzi. "We just need to recover for the final."